RFC: DLMF Content Dictionaries Work in Progress 2 Naming conventions

Appendix A Macros sorted by Content Dictionary

	CD:Name	Notation	Signature	Declared	Proper Name
DLMF_AI.ocd Airy and Related Functions
	AiryAi ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ airy:Ai)
		$\mathrm{Ai}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	§9.2(i)	the Airy function $\mathrm{Ai}$
	AiryBi ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ airy:Bi)
		$\mathrm{Bi}\left(z\right)$	"	"	the Airy function $\mathrm{Bi}$
	ScorerGi
		$\mathrm{Gi}\left(z\right)$	"	(9.12.4)	the Scorer (or inhomogeneous Airy) function $\mathrm{Gi}$
	ScorerHi
		$\mathrm{Hi}\left(z\right)$	"	(9.12.5)	the Scorer (or inhomogeneous Airy) function $\mathrm{Hi}$
DLMF_AI_gen.ocd Airy and Related Functions – Generalizations
	genAiryODEA
		$A_{n}\left(z\right)$	${{\mathbb{Z}^{+}}\times\mathbb{C}\to\mathbb{C}}$	§9.13(i)	the generalized Airy function (ODE) $A_{n}$
	genAiryODEB
		$B_{n}\left(z\right)$	"	"	the generalized Airy function (ODE) $B_{n}$
	genAiryintA
		$A_{k}\left(z,p\right)$	${{\mathbb{Z}^{+}}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§9.13(ii)	the generalized Airy function (integral) $A_{k}$
	genAiryintB
		$B_{k}\left(z,p\right)$	"	"	the generalized Airy function (integral) $B_{k}$
DLMF_AI_mag.ocd Airy and Related Functions – Magnitudes, Phases
	AirymodM
		$M\left(x\right)$	${\mathbb{R}\to\mathbb{R}}$	(9.8.3)	the modulus of Airy functions
	AirymodderivN
		$N\left(x\right)$	"	(9.8.7)	the modulus of derivatives of Airy functions
	Airyphasederivphi
		$\phi\left(x\right)$	"	(9.8.8)	the phase of derivatives of Airy functions
	Airyphasetheta
		$\theta\left(x\right)$	"	(9.8.4)	the phase of Airy functions
	envAiryAi
		$\mathrm{envAi}\left(x\right)$	"	§2.8(iii)	the envelope of the Airy function $\mathrm{Ai}$
	envAiryBi
		$\mathrm{envBi}\left(x\right)$	"	"	the envelope of the Airy function $\mathrm{Bi}$
DLMF_AI_z.ocd Airy and Related Functions – Zeros
	zAirya	$a_{k}$	${{\mathbb{Z}^{+}}\to\mathbb{R}}$	§9.9(i)	the $k$ ^th zero of Airy $\mathrm{Ai}$
	zAiryb	$b_{k}$	"	"	the $k$ ^th zero of Airy $\mathrm{Bi}$
	zAirybeta
		$\beta_{k}$	${{\mathbb{Z}^{+}}\to\mathbb{C}}$	§9.9(i)	the $k$ ^th complex zero of Airy $\mathrm{Bi}$
	zderivAirya
		$a^{\prime}_{k}$	${{\mathbb{Z}^{+}}\to\mathbb{R}}$	§9.9(i)	the $k$ ^th zero of Airy $\mathrm{Ai}'$
	zderivAiryb
		$b^{\prime}_{k}$	"	"	the $k$ ^th zero of Airy $\mathrm{Bi}'$
	zderivAirybeta
		$\beta^{\prime}_{k}$	${{\mathbb{Z}^{+}}\to\mathbb{C}}$	§9.9(i)	the $k$ ^th complex zero of Airy $\mathrm{Bi}'$
DLMF_BP.ocd Bernoulli and Euler Polynomials
	BernoullinumberB
		$B_{n}$	${{\mathbb{Z}^{*}}\to\mathbb{Q}}$	§24.2(i)	the Bernoulli number
	BernoullipolyB
		$B_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	"	the Bernoulli polynomial
	EulernumberE
		$E_{n}$	${{\mathbb{Z}^{*}}\to\mathbb{Z}}$	§24.2(ii)	the Euler number
	EulerpolyE
		$E_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	"	the Euler polynomial
DLMF_BP_gen.ocd Bernoulli and Euler Polynomials – Generalizations
	genBernoullipolyB
		$B^{(\ell)}_{n}\left(x\right)$	${\mathbb{Z}\times{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§24.16	the generalized Bernoulli polynomial
	genEulerpolyE
		$E^{(\ell)}_{n}\left(x\right)$	"	"	the generalized Euler polynomial
DLMF_BP_per.ocd Bernoulli and Euler Polynomials – Periodic
	perBernoulliB
		$\widetilde{B}_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§24.2(iii)	the periodic Bernoulli function
	perEulerE
		$\widetilde{E}_{n}\left(x\right)$	"	"	the periodic Euler function
DLMF_BP_q.ocd Bernoulli and Euler Polynomials – $q$ -analogues
	qBernoullipolybeta
		$\beta_{n}\left(x,q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{D}\to\mathbb{C}}$	(17.3.7)	the $q$ -Bernoulli polynomial
	qEulernumberA
		$A_{m,s}\left(q\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{D}\to\mathbb{C}}$	(17.3.8)	the $q$ -Euler number
DLMF_BS.ocd Bessel Functions
	BesselJ	$J_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(10.2.2)	the Bessel function of the first kind
	BesselY	$Y_{\nu}\left(z\right)$	"	(10.2.3)	the Bessel function of the second kind
	HankelH1
		${H^{(1)}_{\nu}}\left(z\right)$	"	(10.2.5)	the Hankel function of the first kind(or Bessel function of the third kind)
	HankelH2
		${H^{(2)}_{\nu}}\left(z\right)$	"	(10.2.6)	the Hankel function of the second kind(or Bessel function of the third kind)
DLMF_BS_Kelvin.ocd Bessel Functions – Kelvin
	Kelvinbei
		$\operatorname{bei}_{\nu}\left(x\right)$	${\mathbb{R}\times\mathbb{R}\to\mathbb{C}}$	(10.61.1)	the Kelvin function $\operatorname{bei}_{\nu}$
	Kelvinber
		$\operatorname{ber}_{\nu}\left(x\right)$	"	"	the Kelvin function $\operatorname{ber}_{\nu}$
	Kelvinkei
		$\operatorname{kei}_{\nu}\left(x\right)$	"	(10.61.2)	the Kelvin function $\operatorname{kei}_{\nu}$
	Kelvinker
		$\operatorname{ker}_{\nu}\left(x\right)$	"	"	the Kelvin function $\operatorname{ker}_{\nu}$
DLMF_BS_aux.ocd Bessel Functions – Auxiliary
	BesselJimag
		$\widetilde{J}_{\nu}\left(x\right)$	${\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	§10.24	the Bessel function of the first kind of imaginary order
	BesselYimag
		$\widetilde{Y}_{\nu}\left(x\right)$	"	§10.24	the Bessel function of the second kind of imaginary order
	BickleyKi
		$\mathrm{Ki}_{\alpha}\left(x\right)$	${\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	(10.43.11)	the Bickley function
	NeumannpolyQ
		$O_{n}\left(x\right)$	${{\mathbb{Z}^{+}}\times\mathbb{R}\to\mathbb{R}}$	(10.23.12)	Neumann’s polynomial
	Rayleighsigma
		$\sigma_{n}\left(\nu\right)$	"	(10.21.55)	the Rayleigh function
	modBesselIimag
		$\widetilde{I}_{\nu}\left(x\right)$	${\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(10.45.2)	the modified Bessel function of the first kind of imaginary order
	modBesselKimag
		$\widetilde{K}_{\nu}\left(x\right)$	"	"	the modified Bessel function of the second kind of imaginary order
DLMF_BS_gen.ocd Bessel Functions – Generalizations
	MittagLefflerE
		$E_{a,b}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(10.46.3)	the Mittag-Leffler function
	genBesselphi
		$\phi\left(\rho,\beta;z\right)$	"	(10.46.1)	the generalized Bessel function
DLMF_BS_mag.ocd Bessel Functions – Magnitudes, Phases
	BesselC	$\mathscr{C}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§10.2	the Bessel cylinder function
	HankelmodM
		$M_{\nu}\left(x\right)$	${\mathbb{C}\times\mathbb{R}\to\mathbb{R}}$	(10.18.1)	the modulus of the Hankel function of the first kind
	HankelmodderivN
		$N_{\nu}\left(x\right)$	"	(10.18.2)	the modulus of derivatives of the Hankel function of the first kind
	Hankelphasederivphi
		$\phi_{\nu}\left(x\right)$	"	(10.18.3)	the phase of derivatives of the Hankel function of the first kind
	Hankelphasetheta
		$\theta_{\nu}\left(x\right)$	"	"	the phase of the Hankel function of the first kind
	envBesselJ
		$\mathrm{env}\mskip-2.0mu J_{\nu}\left(x\right)$	"	§2.8(iv)	the envelope of the Bessel function $J_{\nu}$
	envBesselY
		$\mathrm{env}\mskip-2.0mu Y_{\nu}\left(x\right)$	"	"	the envelope of the Bessel function $Y_{\nu}$
DLMF_BS_mat.ocd Bessel Functions – Matrix arguments
	BesselAmat
		$A_{\nu}\left(\mathbf{T}\right)$	${\mathbb{C}\times{\mathbb{R}}^{\bullet\times\bullet}\to\mathbb{C}}$	§35.5(i)	the Bessel function of matrix argument (first kind)
	BesselBmat
		$B_{\nu}\left(\mathbf{T}\right)$	"	(35.5.3)	the Bessel function of matrix argument (second kind)
DLMF_BS_mod.ocd Bessel Functions – Modified
	modBesselI
		$I_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(10.25.2)	the modified Bessel function of the first kind
	modBesselK
		$K_{\nu}\left(z\right)$	"	(10.25.3)	the modified Bessel function of the second kind
	modcylinder
		$\mathscr{Z}_{\nu}\left(z\right)$	"	§10.25	the modified cylinder function
DLMF_BS_modsph.ocd Bessel Functions – Modified Spherical
	modsphBesselK
		$\mathsf{k}_{n}\left(z\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\to\mathbb{C}}$	(10.47.9)	the modified spherical Bessel function $\mathsf{k}_{n}$
	modsphBesseli1
		${\mathsf{i}^{(1)}_{n}}\left(z\right)$	"	(10.47.7)	the modified spherical Bessel function ${\mathsf{i}^{(1)}_{n}}$
	modsphBesseli2
		${\mathsf{i}^{(2)}_{n}}\left(z\right)$	"	(10.47.8)	the modified spherical Bessel function ${\mathsf{i}^{(2)}_{n}}$
DLMF_BS_sph.ocd Bessel Functions – Spherical
	sphBesselJ
		$\mathsf{j}_{n}\left(z\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\to\mathbb{C}}$	(10.47.3)	the spherical Bessel function of the first kind
	sphBesselY
		$\mathsf{y}_{n}\left(z\right)$	"	(10.47.4)	the spherical Bessel function of the second kind
	sphHankel2
		${\mathsf{h}^{(2)}_{n}}\left(z\right)$	"	(10.47.6)	the spherical Hankel function of the second kind
	sphHankelh1
		${\mathsf{h}^{(1)}_{n}}\left(z\right)$	"	(10.47.5)	the spherical Hankel function of the first kind
DLMF_BS_z.ocd Bessel Functions – Zeros
	zBesselj
		$j_{\nu,m}$	${\mathbb{R}\times{\mathbb{Z}^{+}}\to\mathbb{R}}$	§10.21(i)	the $m$ ^th zero of the Bessel function of the first kind $J_{\nu}$
	zBessely
		$y_{\nu,m}$	"	"	the $m$ ^th zero of the Bessel function of the second kind $Y_{\nu}$
	zderivBesselj
		${j^{\prime}_{\nu,m}}$	"	"	the $m$ ^th zero of the derivative of the Bessel function of the first kind $J_{\nu}'$
	zderivBessely
		${y^{\prime}_{\nu,m}}$	"	"	the $m$ ^th zero of the derivative of the Bessel function of the second kind $Y_{\nu}'$
DLMF_CH.ocd Confluent Hypergeometric Functions
	KummerconfhyperM ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo1:hypergeometric1F1)
		$M\left(a,b,z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(13.2.2)	the Kummer confluent hypergeometric function $M$
	KummerconfhyperU
		$U\left(a,b,z\right)$	"	(13.2.6)	the Kummer confluent hypergeometric function $U$
	OlverconfhyperM
		${\mathbf{M}}\left(a,b,z\right)$	"	(13.2.3)	Olver’s confluent hypergeometric function
	WhittakerconfhyperM
		$M_{\kappa,\mu}\left(z\right)$	"	(13.14.2)	the Whittaker confluent hypergeometric function $M_{\kappa,\mu}$
	WhittakerconfhyperW
		$W_{\kappa,\mu}\left(z\right)$	"	(13.14.3)	the Whittaker confluent hypergeometric function $W_{\kappa,\mu}$
DLMF_CH_mat.ocd Confluent Hypergeometric Functions – Matrix arguments
	genhyperPsimat
		$\Psi\left(a;b;\mathbf{T}\right)$	${\mathbb{C}\times\mathbb{C}\times{\mathbb{C}}^{\bullet\times\bullet}\to\mathbb% {C}}$	(35.6.2)	the confluent hypergeometric function of matrix argument (second kind)
DLMF_CH_q.ocd Confluent Hypergeometric Functions – $q$ -analogues
	qPochhammer
		$\left(a;q\right)_{n}$	${\mathbb{C}\times\mathbb{D}\times{\mathbb{Z}^{*}}\to\mathbb{C}}$	§17.2(i)	the $q$ -Pochhammer symbol (or $q$ -shifted factorial)
	qmultiPochhammersym
		$\left(a_{1},a_{2},\ldots,a_{k};q\right)_{n}$
			${{\mathbb{C}}^{\bullet}\times\mathbb{D}\times{\mathbb{Z}^{*}}\to\mathbb{C}}$	"	the $q$ -multiple Pochhammer symbol
DLMF_CM.ocd Combinatorial Analysis
	Bellnumber ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ combinat1:Bell)
		$B\left(n\right)$	${\mathbb{Z}\to\mathbb{Z}}$	§26.7(i)	the Bell number
	Catalannumber
		$C\left(n\right)$	"	(26.5.1)	the Catalan number
	Euleriannumber
		$\genfrac{<}{>}{0.0pt}{}{n}{k}$	${\mathbb{Z}\times\mathbb{Z}\to\mathbb{Z}}$	§26.14(i)	the Eulerian number
	LeviCivitasym
		$\epsilon_{ijk}$	${\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}\to\left\{0,\pm 1\right\}}$
				(1.6.14)	the Levi-Civita symbol
	Pochhammersym ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo0:pochhammer)
		${\left(a\right)_{n}}$	${\mathbb{C}\times{\mathbb{Z}^{*}}\to\mathbb{C}}$	§5.2(iii)	the Pochhammer symbol (or shifted factorial)
	StirlingnumberS ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ combinat1:Stirling_S)
		$S\left(n,k\right)$	${\mathbb{Z}\times\mathbb{Z}\to\mathbb{Z}}$	§26.8(i)	the Stirling number of the second kind
	Stirlingnumbers ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ combinat1:Stirling_s)
		$s\left(n,k\right)$	"	§26.8(i)	the Stirling number of the first kind
	binom ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ combinat1:binomial)
		$\genfrac{(}{)}{0.0pt}{}{z}{m}$	${\mathbb{C}\times\mathbb{Z}\to\mathbb{C}}$	§1.2(i)	the binomial coefficient
	multinomial ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ combinat1:multinomial)
		$\genfrac{(}{)}{0.0pt}{}{n}{n_{1},n_{2},\ldots,n_{k}}$	${\mathbb{Z}\times{\mathbb{Z}}^{\bullet}\to\mathbb{Z}}$	§26.4(i)	the multinomial coefficient
	ncompositions
		$c\left(n\right)$	${\mathbb{Z}\to\mathbb{Z}}$	§26.11	the number of compositions of $n$
		$c_{m}\left(n\right)$	${\mathbb{Z}\times\mathbb{Z}\to\mathbb{Z}}$		the number of compositions of $n$ into exactly $m$ parts
	npartitions
		$p\left(n\right)$		§26.2	the total number of partitions of $n$
		$p_{m}\left(n\right)$	${\mathbb{Z}\times\mathbb{Z}\to\mathbb{Z}}$	§26.9(i)	the total number of partitions of $n$ into at most $m$ parts
	npermutations
		$\mathfrak{S}_{n}$	${\mathbb{Z}\to\mathbb{Z}}$	§26.13	the number of permutations of $n$
	nplanepartitions
		$\mathrm{pp}\left(n\right)$	"	§26.12(i)	the number of plane partitions of $n$
	nrestcompositions
		$c\left(\mathrm{condition},n\right)$
			${C\to\mathbb{Z}\mbox{ where $C$ is a condition, see text}}$
				§26.11	the restricted number of compositions of $n$ into exactly $m$ parts
	nrestpartitions
		$p\left(\mathrm{condition},n\right)$
			"	§26.10(i)	the restricted number of partitions of $n$
		$p_{m}\left(\mathrm{condition},n\right)$
			${\mathbb{Z}\times C\to\mathbb{Z}\mbox{ where $C$ is a condition, see text}}$
				§26.9(i)	the restricted number of partitions of $n$ into at most $m$ parts
DLMF_CM_q.ocd Combinatorial Analysis – $q$ -analogues
	idem	$\mathrm{idem}\left(\chi_{1};\chi_{2}\dots\chi_{n}\right)$
				§17.1	the idem function
	qStirlingnumbera
		$a_{m,s}\left(q\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{D}\to\mathbb{C}}$	(17.3.9)	the $q$ -Stirling number
	qbinom	$\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}$	"	(17.2.27)	the $q$ -binomial coefficient
	qfactorial
		$n!_{q}$	${{\mathbb{Z}^{*}}\times\mathbb{D}\to\mathbb{C}}$	(5.18.2)	the $q$ -factorial
	qmultinomial
		$\genfrac{[}{]}{0.0pt}{}{n}{n_{1},n_{2},\ldots,n_{k}}_{q}$	${{\mathbb{Z}^{}}\times{{\mathbb{Z}^{}}}^{\bullet}\times\mathbb{D}\to\mathbb{% C}}$	§26.16	the $q$ -multinomial coefficient
DLMF_CW.ocd Coulomb Functions
	irregCoulombG
		$G_{\ell}\left(\eta,\rho\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{C}}$	(33.2.11)	the irregular Coulomb (radial) function (for repulsive interactions) $G_{\ell}$
	irregCoulombH
		${H^{\pm}_{\ell}}\left(\eta,\rho\right)$	${\left\{\pm\right\}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to% \mathbb{C}}$	(33.2.7)	the irregular Coulomb (radial) function (for repulsive interactions) ${H^{\pm}_{\ell}}$
	irregCoulombc
		$c\left(\epsilon,\ell;r\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{C}}$	(33.14.9)	the irregular Coulomb (radial) function (for attractive interactions) $c$
	irregCoulombh
		$h\left(\epsilon,\ell;r\right)$	"	(33.14.7)	the irregular Coulomb (radial) function (for attractive interactions) $h$
	regCoulombF
		$F_{\ell}\left(\eta,\rho\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{C}}$	(33.2.3)	the regular Coulomb (radial) function (for repulsive interactions) $F_{\ell}$
	regCoulombf
		$f\left(\epsilon,\ell;r\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{C}}$	(33.14.4)	the regular Coulomb (radial) function (for attractive interactions) $f$
	regCoulombs
		$s\left(\epsilon,\ell;r\right)$	"	(33.14.9)	the regular Coulomb (radial) function (for attractive interactions) $s$
DLMF_CW_mag.ocd Coulomb Functions – Magnitudes, Phases
	Coulombphasesigma
		${\sigma_{\ell}}\left(\eta\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	(33.2.10)	the phase shift of the irregular Coulomb function ${H^{\pm}_{\ell}}$
	Coulombphasetheta
		${\theta_{\ell}}\left(\eta,\rho\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(33.2.9)	the phase of the irregular Coulomb function ${H^{\pm}_{\ell}}$
	Coulombturnr
		$r_{\mathrm{tp}}\left(\epsilon,\ell\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\to\mathbb{R}}$	(33.14.3)	the outer turning point for Coulomb (radial) functions (for repulsive interactions)
	Coulombturnrho
		$\rho_{\mathrm{tp}}\left(\eta,\ell\right)$	"	(33.2.2)	the outer turning point for Coulomb (radial) functions (for attractive interactions)
	envCoulombM
		$M_{\ell}\left(\eta,\rho\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(33.3.1)	the envelope of the Coulomb functions (for repulsive interactions)
	normCoulombC
		$C_{\ell}\left(\eta\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	(33.2.5)	the normalizing constant for Coulomb (radial) function
DLMF_EF.ocd Elementary Functions
	Gudermannian
		$\operatorname{gd}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(4.23.39)	the Gudermannian function
	aGudermannian
		${\operatorname{gd}^{-1}}\left(z\right)$	"	(4.23.41)	the inverse of the Gudermannian function
	acos ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arccos)
		$\operatorname{arccos}\left(z\right)$	"	§4.23(ii)	the inverse of the cosine function
	acosh ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arccosh)
		$\operatorname{arccosh}\left(z\right)$	"	§4.37(ii)	the inverse of the hyperbolic cosine function
	acot ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arccot)
		$\operatorname{arccot}\left(z\right)$	"	(4.23.9)	the inverse of the cotangent function
	acoth ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arccoth)
		$\operatorname{arccoth}\left(z\right)$	"	(4.37.9)	the inverse of the hyperbolic cotangent function
	acsc ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arccsc)
		$\operatorname{arccsc}\left(z\right)$	"	(4.23.7)	the inverse of the cosecant function
	acsch ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arcsch)
		$\operatorname{arccsch}\left(z\right)$	"	(4.37.7)	the inverse of the hyperbolic cosecant function
	asec ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arcsec)
		$\operatorname{arcsec}\left(z\right)$	"	(4.23.8)	the inverse of the secant function
	asech ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arcsech)
		$\operatorname{arcsech}\left(z\right)$	"	(4.37.8)	the inverse of the hyperbolic secant function
	asin ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arcsin)
		$\operatorname{arcsin}\left(z\right)$	"	§4.23(ii)	the inverse of the sine function
	asinh ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arcsinh)
		$\operatorname{arcsinh}\left(z\right)$	"	§4.37(ii)	the inverse of the hyperbolic sine function
	atan ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arctan)
		$\operatorname{arctan}\left(z\right)$	"	§4.23(ii)	the inverse of the tangent function
	atanh ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc1:arctanh)
		$\operatorname{arctanh}\left(z\right)$	"	§4.37(ii)	the inverse of the hyperbolic tangent function
DLMF_EF_lambert.ocd Elementary Functions – lambert
	LambertW
		$W\left(x\right)$	${\mathbb{R}\to\mathbb{R}}$	(4.13.1)	the Lambert $W$ -function
	LambertWm
		$\mathrm{Wm}\left(x\right)$	"	§4.13	the non-principal branch of the Lambert $W$ -function
	LambertWp
		$\mathrm{Wp}\left(x\right)$	"	"	the principal branch of the Lambert $W$ -function
DLMF_EF_mv.ocd Elementary Functions – mv
	Acos ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccos)
		$\operatorname{Arccos}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(4.23.2)	the multivalued inverse of the cosine function
	Acosh ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccosh)
		$\operatorname{Arccosh}\left(z\right)$	"	(4.37.2)	the multivalued inverse of the hyperbolic cosine function
	Acot ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccot)
		$\operatorname{Arccot}\left(z\right)$	"	(4.23.6)	the multivalued inverse of the cotangent function
	Acoth ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccoth)
		$\operatorname{Arccoth}\left(z\right)$	"	(4.37.6)	the multivalued inverse of the hyperbolic cotangent function
	Acsc ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccsc)
		$\operatorname{Arccsc}\left(z\right)$	"	(4.23.4)	the multivalued inverse of the cosecant function
	Acsch ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccsch)
		$\operatorname{Arccsch}\left(z\right)$	"	(4.37.4)	the multivalued inverse of the hyperbolic cosecant function
	Asec ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arccsc)
		$\operatorname{Arcsec}\left(z\right)$	"	(4.23.5)	the multivalued inverse of the secant function
	Asech ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arcsech)
		$\operatorname{Arcsech}\left(z\right)$	"	(4.37.5)	the multivalued inverse of the hyperbolic secant function
	Asin ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arcsin)
		$\operatorname{Arcsin}\left(z\right)$	"	(4.23.1)	the multivalued inverse of the sine function
	Asinh ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arcsinh)
		$\operatorname{Arcsinh}\left(z\right)$	"	(4.37.1)	the multivalued inverse of the hyperbolic sine function
	Atan ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arctan)
		$\operatorname{Arctan}\left(z\right)$	"	(4.23.3)	the multivalued inverse of the tangent function
	Atanh ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:arctanh)
		$\operatorname{Arctanh}\left(z\right)$	"	(4.37.3)	the multivalued inverse of the hyperbolic tangent function
	Ln ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ transc3:ln)
		$\operatorname{Ln}\left(z\right)$	"	(4.2.1)	the multivalued logarithm function
DLMF_EF_q.ocd Elementary Functions – $q$ -analogues
	qCos	$\mathrm{Cos}_{q}\left(x\right)$	${\mathbb{D}\times\mathbb{R}\to\mathbb{C}}$	(17.3.6)	the $q$ -cosine function $\mathrm{Cos}_{q}$
	qExp	$E_{q}\left(x\right)$	"	(17.3.2)	the $q$ -exponential function $E_{q}$
	qSin	$\mathrm{Sin}_{q}\left(x\right)$	"	(17.3.4)	the $q$ -sine function $\mathrm{Sin}_{q}$
	qcos	$\mathrm{cos}_{q}\left(x\right)$	"	(17.3.5)	the $q$ -cosine function $\mathrm{cos}_{q}$
	qexp	$e_{q}\left(x\right)$	"	(17.3.1)	the $q$ -exponential function $e_{q}$
	qsin	$\mathrm{sin}_{q}\left(x\right)$	"	(17.3.3)	the $q$ -sine function $\mathrm{sin}_{q}$
DLMF_EL.ocd Elliptic Integrals
	ccompellintEk
		${E^{\prime}}\left(k\right)$	${\mathbb{C}\to\mathbb{C}}$	(19.2.9)	(Legendre’s) complementary complete elliptic integral of the second kind (of modulus $k$ )
	ccompellintKk
		${K^{\prime}}\left(k\right)$	"	"	(Legendre’s) complementary complete elliptic integral of the first kind (of modulus $k$ )
	compellintDk
		$D\left(k\right)$	"	(19.2.8)	the complete elliptic integral of Janke (of modulus $k$ )
	compellintEk
		$E\left(k\right)$	"	"	(Legendre’s) complete elliptic integral of the second kind (of modulus $k$ )
	compellintKk
		$K\left(k\right)$	"	"	(Legendre’s) complete elliptic integral of the first kind (of modulus $k$ )
	compellintPik
		$\Pi\left(\alpha^{2},k\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	"	(Legendre’s) complete elliptic integral of the third kind (of modulus $k$ )
	incellintDk
		$D\left(\phi,k\right)$	"	(19.2.6)	the incomplete elliptic integral of Janke (of modulus $k$ )
	incellintEk
		$E\left(\phi,k\right)$	"	(19.2.5)	(Legendre’s) incomplete elliptic integral of the second kind (of modulus $k$ )
	incellintFk
		$F\left(\phi,k\right)$	"	(19.2.4)	(Legendre’s) incomplete elliptic integral of the first kind (of modulus $k$ )
	incellintPik
		$\Pi\left(\phi,\alpha^{2},k\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.2.7)	(Legendre’s) incomplete elliptic integral of the third kind (of modulus $k$ )
DLMF_EL_Bulirsch.ocd Elliptic Integrals – Bulirsch
	Bulirschcompellintcel
		$\mathrm{cel}\left(k_{c},p,a,b\right)$
				(19.2.11)	Bulirsch’s complete elliptic integral
	Bulirschincellintel1
		$\mathrm{el1}\left(x,k_{c}\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.2.15)	Bulirsch’s incomplete elliptic integral of the first kind
	Bulirschincellintel2
		$\mathrm{el2}\left(x,k_{c},a,b\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.2.12)	Bulirsch’s incomplete elliptic integral of the second kind
	Bulirschincellintel3
		$\mathrm{el3}\left(x,k_{c},p\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.2.16)	Bulirsch’s incomplete elliptic integral of the third kind
DLMF_EL_Carlson.ocd Elliptic Integrals – Carlson
	CarsonellintRC
		$R_{C}\left(x,y\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.2.17)	Carlson’s elliptic integral combining inverse circular and hyperbolic functions
	Carsonmultivarhyper
		$R_{-a}\left(b_{1},\dots,b_{n};z_{1},\dots,z_{n}\right)$
			${\mathbb{C}\times{\mathbb{C}^{n}}\times{\mathbb{C}^{n}}\to\mathbb{C}}$	(19.16.9)	Carlson’s multivariate hypergeometric function
	CarsonsymellintRD
		$R_{D}\left(x,y,z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.16.5)	Carlson’s elliptic integral symmetric in only two variables
	CarsonsymellintRF
		$R_{F}\left(x,y,z\right)$	"	(19.16.1)	Carlson’s symmetric elliptic integral of first kind
	CarsonsymellintRG
		$R_{G}\left(x,y,z\right)$	"	(19.16.3)	Carlson’s symmetric elliptic integral of second kind
	CarsonsymellintRJ
		$R_{J}\left(x,y,z,p\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(19.16.2)	Carlson’s symmetric elliptic integral of third kind
DLMF_ER.ocd Error Functions, Dawson’s and Fresnel Integrals
	Faddeevaw
		$w\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(7.2.3)	the complementary error function $w$
	erf	$\operatorname{erf}\left(z\right)$	"	(7.2.1)	the error function
	erfc	$\operatorname{erfc}\left(z\right)$	"	(7.2.2)	the complementary error function $\operatorname{erfc}$
	inverf	$\operatorname{inverf}\left(x\right)$	"	(7.17.1)	the inverse error function
	inverfc	$\operatorname{inverfc}\left(x\right)$	"	"	the inverse complementary error function
	repinterfc
		$\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\to\mathbb{C}}$	(7.18.2)	the repeated integrals of complementary error function
DLMF_ER_Fresnel.ocd Error Functions, Dawson’s and Fresnel Integrals – Fresnel
	DawsonintF
		$F\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(7.2.5)	Dawson’s integral
	Fresnelcosint
		$C\left(z\right)$	"	(7.2.7)	the Fresnel cosine integral
	FresnelintF
		$\mathcal{F}\left(z\right)$	"	(7.2.6)	the Fresnel integral
	Fresnelsinint
		$S\left(z\right)$	"	(7.2.8)	the Fresnel sine integral
	GoodwinStatonint
		$G\left(z\right)$	"	(7.2.12)	the Goodwin–Staton integral
	auxFresnelf
		$\mathrm{f}\left(z\right)$	"	?	the auxiliary function for Fresnel integrals $\mathrm{f}$
	auxFresnelg
		$\mathrm{g}\left(z\right)$	"	"	the auxiliary function for Fresnel integrals $\mathrm{g}$
DLMF_ER_Voigt.ocd Error Functions, Dawson’s and Fresnel Integrals – Voight
	FischersHh
		$\mathit{Hh}_{n}\left(z\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\to\mathbb{C}}$	(7.18.12)	Fischer’s probability function
	MillsM	$\mathsf{M}\left(x\right)$	${\mathbb{C}\to\mathbb{C}}$	(7.8.1)	Mill’s ratio
	VoightH	$H\left(a,u\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(7.19.4)	the line broadening function
	VoigtU	$\mathsf{U}\left(x,t\right)$	"	(7.19.1)	the Voigt function $\mathsf{U}$
	VoigtV	$\mathsf{V}\left(x,t\right)$	"	(7.19.2)	the Voigt function $\mathsf{V}$
DLMF_EX.ocd Exponential, Logarithmic, Sine, and Cosine Integrals
	auxsincosintf
		$\mathrm{f}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(6.2.17)	the auxiliary function for sine and cosine integrals $\mathrm{f}$
	auxsincosintg
		$\mathrm{g}\left(z\right)$	"	(6.2.18)	the auxiliary function for sine and cosine integrals $\mathrm{g}$
	coshint	$\mathrm{Chi}\left(z\right)$	"	(6.2.16)	the hyperbolic cosine integral
	cosint	$\mathrm{Ci}\left(z\right)$	"	(6.2.11)	the cosine integral $\mathrm{Ci}$
	cosintCin
		$\mathrm{Cin}\left(z\right)$	"	(6.2.12)	the cosine integral $\mathrm{Cin}$
	expintE	$E_{1}\left(z\right)$	"	(6.2.1)	the exponential integral $E_{1}$
	expintEi ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ expint:expintEi)
		$\mathrm{Ei}\left(z\right)$	"	§6.2(i)	the exponential integral $\mathrm{Ei}$
	expintEin
		$\mathrm{Ein}\left(z\right)$	"	(6.2.3)	the complementary exponential integral
	genexpintE ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ expint:E)
		$E_{p}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(8.19.1)	the generalized exponential integral
	logint ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ expint:logint)
		$\mathrm{li}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(6.2.8)	the logarithmic integral
	shiftsinint
		$\mathrm{si}\left(z\right)$	"	(6.2.10)	the shifted sine integral
	sinhint	$\mathrm{Shi}\left(z\right)$	"	(6.2.15)	the hyperbolic sine integral
	sinint	$\mathrm{Si}\left(z\right)$	"	(6.2.9)	the sine integral $\mathrm{Si}$
DLMF_EX_inc.ocd Exponential, Logarithmic, Sine, and Cosine Integrals – Incomplete
	gencosint
		$\mathrm{Ci}\left(a,z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(8.21.2)	the generalized cosine integral
	genshiftcosint
		$\mathrm{ci}\left(a,z\right)$	"	(8.21.1)	the generalized shifted cosine integral
	genshiftsinint
		$\mathrm{si}\left(a,z\right)$	"	"	the generalized shifted sine integral
	gensinint
		$\mathrm{Si}\left(a,z\right)$	"	(8.21.2)	the generalized sine integral
	incBeta	$\mathrm{B}_{x}\left(a,b\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(8.17.1)	the incomplete beta function
	incGamma
		$\Gamma\left(a,z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(8.2.2)	the upper incomplete gamma function
	incgamma
		$\gamma\left(a,z\right)$	"	(8.2.1)	the lower incomplete gamma function
	normincBetaI
		$I_{x}\left(a,b\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(8.17.2)	the normalized incomplete beta function
	normincGammaP
		$P\left(a,z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(8.2.4)	the normalized incomplete gamma function $P$
	normincGammaQ
		$Q\left(a,z\right)$	"	"	the normalized incomplete gamma function $Q$
	scincgamma
		$\gamma^{*}\left(a,z\right)$	"	(8.2.6)	the scaled incomplete gamma function
	terminant
		$F_{p}\left(z\right)$	"	(2.11.11)	the terminant function
DLMF_EX_mat.ocd Exponential, Logarithmic, Sine, and Cosine Integrals – Matrix arguments
	multivarEulerBeta
		$\mathrm{B}_{m}\left(a,b\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(35.3.3)	multivariate beta function
DLMF_GA.ocd Gamma Function
	BarnesG	$G\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(5.17.1)	the Barne’s $G$ -function (or double gamma) function
	EulerBeta ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo0:beta)
		$\mathrm{B}\left(a,b\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(5.12.1)	the Euler beta function
	EulerGamma ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo0:gamma)
		$\Gamma\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(5.2.1)	the Euler gamma function
	digamma	$\psi\left(z\right)$	"	(5.2.2)	the digamma (or psi) function
	polygamma
		$\psi^{(n)}\left(z\right)$	${{\mathbb{Z}^{+}}\times\mathbb{C}\to\mathbb{C}}$	§5.15	the polygamma function
DLMF_GA_mat.ocd Gamma Function – Matrix arguments
	multivarEulerGamma
		$\Gamma_{m}\left(a\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\to\mathbb{C}}$	§35.3(i)	the multivariate gamma function
DLMF_GA_q.ocd Gamma Function – $q$ -analogues
	qBeta	$\mathrm{B}_{q}\left(a,b\right)$	${\mathbb{D}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(5.18.11)	the $q$ -Beta function
	qDigamma
		$\psi_{q}\left(z\right)$	${\mathbb{D}\times\mathbb{C}\to\mathbb{C}}$	?	the $q$ -digamma function
	qGamma	$\Gamma_{q}\left(z\right)$	"	(5.18.4)	the $q$ -gamma function
	qpolygamma
		$\psi^{(n)}_{q}\left(z\right)$	${{\mathbb{Z}^{+}}\times\mathbb{D}\times\mathbb{C}\to\mathbb{C}}$	?	the $q$ -polygamma function
DLMF_GH.ocd Generalized Hypergeometric Functions and Meijer $G$ -Function
	MeijerG	${G^{m,n}_{p,q}}\left(z;a_{1}\dots,a_{p};b_{1},\dots,b_{q}\right)$
			${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\times{\mathbb{Z}% ^{+}}\times\mathbb{C}\times{\mathbb{C}^{p}}\times{\mathbb{C}^{q}}\to\mathbb{C}}$
				(16.17.1)	the Meijer $G$ -function
	genhyper1F1 ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo1:hypergeometric1F1)
		${{}_{1}F_{1}}\left(a;b;z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§16.2	Kummer confluent hypergeometric function, ${{}_{1}F_{1}}=M$
	genhyper2F1 ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo1:hypergeometric2F1)
		${{}_{2}F_{1}}\left(a,b;c;z\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	"	Gauss’ hypergeometric function, ${{}_{2}F_{1}}=F$
	genhyperF ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo1:hypergeometric_pFq)
		${{}_{p}F_{q}}\left(a_{1},\dots,a_{p};b_{1},\dots,b_{q};z\right)$
			${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\times{\mathbb{C}}^{p}\times{\mathbb{C}% }^{q}\times\mathbb{C}\to\mathbb{C}}$
				"	the generalized hypergeometric function
	genhyperH
		${{}_{p}H_{q}}\left(a_{1},\dots,a_{p};b_{1},\dots,b_{q};z\right)$
			"	(16.4.16)	the bilateral hypergeometric function
	genhyperOlverF
		${{}_{p}{\mathbf{F}}_{q}}\left(a_{1},\dots,a_{p};b_{1},\dots,b_{q};z\right)$
			"	(16.2.5)	Olver’s scaled generalized hypergeometric function
DLMF_GH_Appell.ocd Generalized Hypergeometric Functions and Meijer $G$ -Function – Appell
	AppelF1 ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeon2:appel_F1)
		${F_{1}}\left(\alpha;\beta,\beta^{\prime};\gamma;x,y\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\to\mathbb{C}}$
				(16.13.1)	the first Appell function
	AppelF2 ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeon2:appel_F2)
		${F_{2}}\left(\alpha;\beta,\beta^{\prime};\gamma,\gamma^{\prime};x,y\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				(16.13.2)	the second Appell function
	AppelF3 ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeon2:appel_F3)
		${F_{3}}\left(\alpha,\alpha^{\prime};\beta,\beta^{\prime};\gamma;x,y\right)$
			"	(16.13.3)	the third Appell function
	AppelF4 ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeon2:appel_F4)
		${F_{4}}\left(\alpha,\beta;\gamma,\gamma^{\prime};x,y\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\to\mathbb{C}}$
				(16.13.4)	the fourth Appell function
DLMF_GH_mat.ocd Generalized Hypergeometric Functions and Meijer $G$ -Function – Matrix arguments
	genhyperFmat
		${{}_{p}F_{q}}\left(a_{1},\dots,a_{p};b_{1},\dots,b_{q};\mathbf{T}\right)$
			${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times{\mathbb{C}}^{p}\times{\mathbb{C}% }^{q}\times{\mathbb{C}}^{\bullet\times\bullet}\to\mathbb{C}}$
				(35.8.1)	the generalized hypergeometric function of matrix argument
DLMF_GH_q.ocd Generalized Hypergeometric Functions and Meijer $G$ -Function – $q$ -analogues
	qgenhyperphi
		${{}_{r+1}\phi_{s}}\left(a_{0},\dots,a_{r};b_{1},\dots,b_{s};q,z\right)$
			${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times{\mathbb{C}}^{r}\times{\mathbb{C}% }^{s}\times\mathbb{D}\times\mathbb{C}\to\mathbb{C}}$
				(17.4.1)	the $q$ -hypergeometric (or basic hypergeometric) function
	qgenhyperpsi
		${{}_{r}\psi_{s}}\left(a_{0},\dots,a_{r};b_{1},\dots,b_{s};q,z\right)$
			"	(17.4.3)	the bilateral $q$ -hypergeometric (or bilateral basic hypergeometric) function
DLMF_GH_qAppell.ocd Generalized Hypergeometric Functions and Meijer $G$ -Function – $q$ -Appell
	qAppelPhi1
		$\Phi^{(1)}\left(a;b,b^{\prime};c;q;x,y\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				(17.4.5)	the first $q$ -Appell function
	qAppelPhi2
		$\Phi^{(2)}\left(a;b,b^{\prime};c,c^{\prime};q;x,y\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				(17.4.6)	the second $q$ -Appell function
	qAppelPhi3
		$\Phi^{(3)}\left(a,a^{\prime};b,b^{\prime};c;q;x,y\right)$
			"	(17.4.7)	the third $q$ -Appell function
	qAppelPhi4
		$\Phi^{(4)}\left(a,b;c,c^{\prime};q;x,y\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				(17.4.8)	the fourth $q$ -Appell function
DLMF_HE.ocd Heun Functions
	HeunHf	$(s_{1},s_{2})\mathit{Hf}_{m}\left(a,q_{m};\alpha,\beta,\gamma,\delta;z\right)$
			${\mathbb{C}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times% \mathbb{C}\to\mathbb{C}}$
				§31.4	the Heun function
		$(s_{1},s_{2})\mathit{Hf}_{m}^{\nu}\left(a,q_{m};\alpha,\beta,\gamma,\delta;z\right)$
	HeunHl	$\mathit{H\!\ell}\left(a,q;\alpha,\beta,\gamma,\delta;z\right)$
			${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}% \times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				(31.3.1)	the (fundamental) Heun function
	HeunpolyHp
		$\mathit{Hp}_{n,m}\left(a,q_{n,m};-n,\beta,\gamma,\delta;z\right)$
			${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{C}\times\mathbb{C}\times{% \mathbb{Z}^{*}}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C% }\to\mathbb{C}}$
				(31.5.2)	the Heun polynomial
DLMF_HY.ocd Hypergeometric Function
	Jacobiphi
		$\phi^{(\alpha,\beta)}_{\lambda}\left(t\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	(15.9.11)	the Jacobi function
	RiemannsymP
		$P\begin{Bmatrix}a&b&c&\cr a_{1}&b_{1}&c_{1}&z\cr a_{2}&b_{2}&c_{2}&\end{Bmatrix}$	${{\mathbb{C}^{9}}\times\mathbb{C}\to\mathbb{C}}$	(15.11.3)	Riemann’s $P$ -symbol for solutions of the generalized hypergeometric differential equation
	hyperF ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeo1:hypergeometric2F1)
		$F\left(a,b;c;z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(15.2.1)	(Gauss’) hypergeometric function
	hyperOlverF
		$\mathbf{F}\left(a,b;c;z\right)$	"	(15.2.2)	Olver’s scaled hypergeometric function
DLMF_IC.ocd Integrals with Coalescing Saddles
	canonint
		$\Psi_{K}\left(\mathbf{x}\right)$	${{\mathbb{Z}^{*}}\times{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.4)	the canonical integral function
	cuspcatastrophe
		$\Phi_{K}\left(t;\mathbf{x}\right)$	${{\mathbb{Z}^{*}}\times\mathbb{C}\times{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.1)	the cuspoid catastrophe of codimension $K$
	diffrcanonint
		$\Psi_{K}(\mathbf{x};k)$	${{\mathbb{Z}^{*}}\times{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.10)	the diffraction canonical integral
	ellumbcanonint
		$\Psi^{(\mathrm{E})}\left(\mathbf{x}\right)$	${{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.5)	the elliptic umbilic canonical integral function
	ellumbcatastrophe
		$\Phi^{(\mathrm{E})}\left(s,t;\mathbf{x}\right)$	${\mathbb{C}\times\mathbb{C}\times{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.2)	the elliptic umbilic catastrophe
	ellumbdiffrcanonint
		$\Psi^{(\mathrm{E})}(\mathbf{x};k)$	${{\mathbb{R}}^{K}\times\mathbb{R}\to\mathbb{C}}$	(36.2.11)	the elliptic umbilic diffraction canonical integral function
	hyperumbcanonint
		$\Psi^{(\mathrm{H})}\left(\mathbf{x}\right)$	${{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.5)	the hyperbolic umbilic canonical integral function
	hyperumbcatastrophe
		$\Phi^{(\mathrm{H})}\left(s,t;\mathbf{x}\right)$	${\mathbb{C}\times\mathbb{C}\times{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.3)	the hyperbolic umbilic catastrophe
	hyperumbdiffrcanonint
		$\Psi^{(\mathrm{H})}(\mathbf{x};k)$	${{\mathbb{R}}^{K}\times\mathbb{R}\to\mathbb{C}}$	(36.2.11)	the hyperbolic umbilic diffraction canonical integral function
	umbcanonint
		$\Psi^{(\mathrm{U})}\left(\mathbf{x}\right)$	${{\mathbb{R}}^{K}\to\mathbb{C}}$	(36.2.5)	the umbilic canonical integral function
	umbcatastrophe
		$\Phi^{(\mathrm{U})}\left(s,t;\mathbf{x}\right)$	${\mathbb{C}\times\mathbb{C}\times{\mathbb{R}}^{K}\to\mathbb{C}}$	§36.2	the umbilic catastrophe
	umbdiffrcanonint
		$\Psi^{(\mathrm{U})}(\mathbf{x};k)$	${{\mathbb{R}}^{K}\times\mathbb{R}\to\mathbb{C}}$	(36.2.11)	the umbilic diffraction canonical integral function
DLMF_JA.ocd Jacobian Elliptic Functions
	Jacobiamk
		$\operatorname{am}\left(x,k\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(22.16.1)	the Jacobi’s amplitude function (of modulus $k$ )
	Jacobiellcdk
		$\operatorname{cd}\left(u,k\right)$	"	(22.2.8)	the Jacobian elliptic function $\operatorname{cd}$ (of modulus $k$ )
	Jacobiellcnk
		$\operatorname{cn}\left(u,k\right)$	"	(22.2.5)	the Jacobian elliptic function $\operatorname{cn}$ (of modulus $k$ )
	Jacobiellcsk
		$\operatorname{cs}\left(u,k\right)$	"	(22.2.9)	the Jacobian elliptic function $\operatorname{cs}$ (of modulus $k$ )
	Jacobielldck
		$\operatorname{dc}\left(u,k\right)$	"	(22.2.8)	the Jacobian elliptic function $\operatorname{dc}$ (of modulus $k$ )
	Jacobielldnk
		$\operatorname{dn}\left(u,k\right)$	"	(22.2.6)	the Jacobian elliptic function $\operatorname{dn}$ (of modulus $k$ )
	Jacobielldsk
		$\operatorname{ds}\left(u,k\right)$	"	(22.2.7)	the Jacobian elliptic function $\operatorname{ds}$ (of modulus $k$ )
	Jacobiellnck
		$\operatorname{nc}\left(u,k\right)$	"	(22.2.5)	the Jacobian elliptic function $\operatorname{nc}$ (of modulus $k$ )
	Jacobiellndk
		$\operatorname{nd}\left(u,k\right)$	"	(22.2.6)	the Jacobian elliptic function $\operatorname{nd}$ (of modulus $k$ )
	Jacobiellnsk
		$\operatorname{ns}\left(u,k\right)$	"	(22.2.4)	the Jacobian elliptic function $\operatorname{ns}$ (of modulus $k$ )
	Jacobiellsck
		$\operatorname{sc}\left(u,k\right)$	"	(22.2.9)	the Jacobian elliptic function $\operatorname{sc}$ (of modulus $k$ )
	Jacobiellsdk
		$\operatorname{sd}\left(u,k\right)$	"	(22.2.7)	the Jacobian elliptic function $\operatorname{sd}$ (of modulus $k$ )
	Jacobiellsnk
		$\operatorname{sn}\left(u,k\right)$	"	(22.2.4)	the Jacobian elliptic function $\operatorname{sn}$ (of modulus $k$ )
	aJacobiellcdk
		$\operatorname{arccd}\left(x,k\right)$	"	§22.15(i)	the inverse of the Jacobian elliptic function $\operatorname{cd}$ (of modulus $k$ )
	aJacobiellck
		$\operatorname{arcdc}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{dc}$ (of modulus $k$ )
	aJacobiellcnk
		$\operatorname{arccn}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{cn}$ (of modulus $k$ )
	aJacobiellcsk
		$\operatorname{arccs}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{cs}$ (of modulus $k$ )
	aJacobielldnk
		$\operatorname{arcdn}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{dn}$ (of modulus $k$ )
	aJacobielldsk
		$\operatorname{arcds}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{ds}$ (of modulus $k$ )
	aJacobiellnck
		$\operatorname{arcnc}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{nc}$ (of modulus $k$ )
	aJacobiellndk
		$\operatorname{arcnd}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{nd}$ (of modulus $k$ )
	aJacobiellnsk
		$\operatorname{arcns}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{ns}$ (of modulus $k$ )
	aJacobiellsck
		$\operatorname{arcsc}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{sc}$ (of modulus $k$ )
	aJacobiellsdk
		$\operatorname{arcsd}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{ds}$ (of modulus $k$ )
	aJacobiellsnk
		$\operatorname{arcsn}\left(x,k\right)$	"	"	the inverse of the Jacobian elliptic function $\operatorname{sn}$ (of modulus $k$ )
DLMF_JA_aux.ocd Jacobian Elliptic Functions – Auxiliary
	JacobiEpsilonk
		$\mathcal{E}\left(x,k\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(22.16.14)	Jacobi’s Epsilon function (of modulus $k$ )
	JacobiZetak
		$\mathrm{Z}\left(x\|k\right)$	"	(22.16.32)	Jacobi’s Zeta function (of modulus $k$ )
DLMF_JA_gen.ocd Jacobian Elliptic Functions – Generalizations
	agenJacobiellk
		$\operatorname{arcpq}\left(x,k\right)$
			${\left\{\mathrm{s},\mathrm{n},\mathrm{d}\right\}\times\left\{\mathrm{s},% \mathrm{n},\mathrm{d}\right\}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				?	the inverse of the generic Jacobian elliptic function $\operatorname{pq}$ (of modulus $k$ )
	genJacobiellk
		$\operatorname{pq}\left(u,k\right)$	"	(22.2.10)	the generic Jacobian elliptic function $\operatorname{pq}$ (of modulus $k$ )
DLMF_LA.ocd Lam’e Functions
	LameEc	$\mathit{Ec}^{m}_{\nu}\left(z,k^{2}\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	§29.3(iv)	the Lamé function $\mathit{Ec}^{m}_{\nu}$
	LameEs	$\mathit{Es}^{m}_{\nu}\left(z,k^{2}\right)$	"	"	the Lamé function $\mathit{Es}^{m}_{\nu}$
	Lameeigvala
		$a^{n}_{\nu}\left(k^{2}\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{C}}$	§29.3(i)	the eigenvalues of Lamé’s equation $a^{n}_{\nu}$
	Lameeigvalb
		$b^{n}_{\nu}\left(k^{2}\right)$	"	"	the eigenvalues of Lamé’s equation $b^{n}_{\nu}$
	LamepolycE
		$\mathit{cE}^{m}_{2n+1}\left(z,k^{2}\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{C}\times\mathbb{R}\to% \mathbb{C}}$	(29.12.3)	the Lamé polynomial $\mathit{cE}^{m}_{2n+1}$
	LamepolycdE
		$\mathit{cdE}^{m}_{2n+2}\left(z,k^{2}\right)$	"	(29.12.7)	the Lamé polynomial $\mathit{cdE}^{m}_{2n+2}$
	LamepolydE
		$\mathit{dE}^{m}_{2n+1}\left(z,k^{2}\right)$	"	(29.12.4)	the Lamé polynomial $\mathit{dE}^{m}_{2n+1}$
	LamepolysE
		$\mathit{sE}^{m}_{2n+1}\left(z,k^{2}\right)$	"	(29.12.2)	the Lamé polynomial $\mathit{sE}^{m}_{2n+1}$
	LamepolyscE
		$\mathit{scE}^{m}_{2n+2}\left(z,k^{2}\right)$	"	(29.12.5)	the Lamé polynomial $\mathit{scE}^{m}_{2n+2}$
	LamepolyscdE
		$\mathit{scdE}^{m}_{2n+3}\left(z,k^{2}\right)$	"	(29.12.8)	the Lamé polynomial $\mathit{scdE}^{m}_{2n+3}$
	LamepolysdE
		$\mathit{sdE}^{m}_{2n+2}\left(z,k^{2}\right)$	"	(29.12.6)	the Lamé polynomial $\mathit{sdE}^{m}_{2n+2}$
	LamepolyuE
		$\mathit{uE}^{m}_{2n}\left(z,k^{2}\right)$	"	(29.12.1)	the Lamé polynomial $\mathit{uE}^{m}_{2n}$
DLMF_LE.ocd Legendre and Related Functions
	DunsterQ
		$\widehat{\mathsf{Q}}^{-\mu}_{-\tfrac{1}{2}+\mathrm{i}\tau}\left(x\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	(14.20.2)	Dunster’s conical function
	FerrersP
		$\mathsf{P}_{\nu}\left(x\right)$	${\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	§14.2(ii)	$=\mathsf{P}^{0}_{\nu}$ , shorthand for the Ferrers function of the first kind
		$\mathsf{P}^{\mu}_{\nu}\left(x\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	(14.3.1)	the Ferrers function of the first kind
	FerrersQ
		$\mathsf{Q}_{\nu}\left(x\right)$	${\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	§14.2(ii)	$=\mathsf{Q}^{0}_{\nu}$ , shorthand for the Ferrers function of the second kind
		$\mathsf{Q}^{\mu}_{\nu}\left(x\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	(14.3.2)	the Ferrers function of the second kind
	assLegendreOlverQ
		$\boldsymbol{Q}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§14.2(ii)	$=\boldsymbol{Q}^{0}_{\nu}$ , shorthand for Olver’s associated Legendre function
		$\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§14.21(i)	Olver’s associated Legendre function
	assLegendreP
		$P_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§14.2(ii)	$=P^{0}_{\nu}$ , shorthand for the associated Legendre function of the first kind
		$P^{\mu}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§14.21(i)	the associated Legendre function of the first kind
	assLegendreQ
		$Q_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§14.2(ii)	$=Q^{0}_{\nu}$ , shorthand for the associated Legendre function of the second kind
		$Q^{\mu}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§14.21(i)	the associated Legendre function of the second kind
	sphharmonicY
		$Y_{{l},{m}}\left(\theta,\phi\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\to% \mathbb{C}}$	(14.30.1)	the spherical harmonic
	surfharmonicY
		$Y_{l}^{m}\left(\theta,\phi\right)$	"	(14.30.2)	the surface harmonic of the first kind
DLMF_MA.ocd Mathieu Functions and Hill’s Equation
	Mathieuce
		$\mathrm{ce}_{n}\left(z,q\right)$	${\mathbb{Z}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§28.2(vi)	the Mathieu function $\mathrm{ce}_{n}$
	Mathieueigvala
		$a_{n}\left(q\right)$	${\mathbb{Z}\times\mathbb{C}\to\mathbb{C}}$	§28.2(v)	the eigenvalues of the Mathieu’s equation $a_{n}$
	Mathieueigvalb
		$b_{n}\left(q\right)$	"	"	the eigenvalues of the Mathieu’s equation $b_{n}$
	Mathieueigvallambda
		$\lambda_{\nu+2n}\left(q\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§28.12(i)	the eigenvalues of Mathieu’s equation $\lambda_{\nu+2n}$
	Mathieufe
		$\mathrm{fe}_{n}\left(z,q\right)$	${\mathbb{Z}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(28.5.1)	the second solution of Mathieu’s equation $\mathrm{fe}_{n}$
	Mathieuge
		$\mathrm{ge}_{n}\left(z,q\right)$	"	(28.5.2)	the second solution of Mathieu’s equation $\mathrm{ge}_{n}$
	Mathieume
		$\mathrm{me}_{n}\left(z,q\right)$	"	§28.12(ii)	the Mathieu function $\mathrm{me}_{n}$
	Mathieuse
		$\mathrm{se}_{n}\left(z,q\right)$	"	§28.2(vi)	the Mathieu function $\mathrm{se}_{n}$
DLMF_MA_cross.ocd Mathieu Functions and Hill’s Equation – Cross-Products
	modMathieuD
		$\mathrm{D}_{j}\left(\nu,\mu,z\right)$	${\mathbb{Z}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(28.28.24)	the cross-products of modified Mathieu functions and their derivatives
	radMathieuDc
		$\mathrm{Dc}_{j}\left(n,m,z\right)$	${\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}\times\mathbb{C}\to\mathbb{C}}$	(28.28.39)	the cross-products of radial Mathieu functions and their derivatives $\mathrm{Dc}_{j}$
	radMathieuDs
		$\mathrm{Ds}_{j}\left(n,m,z\right)$	"	(28.28.35)	the cross-products of radial Mathieu functions and their derivatives $\mathrm{Ds}_{j}$
	radMathieuDsc
		$\mathrm{Dsc}_{j}\left(n,m,z\right)$	"	(28.28.40)	the cross-products of radial Mathieu functions and their derivatives $\mathrm{Dsc}_{j}$
DLMF_MA_mod.ocd Mathieu Functions and Hill’s Equation – Modified
	modMathieuCe
		$\mathrm{Ce}_{\nu}\left(z,q\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(28.20.3)	the modified Mathieu function $\mathrm{Ce}_{\nu}$
	modMathieuFe
		$\mathrm{Fe}_{\nu}\left(z,q\right)$	"	(28.20.6)	the modified Mathieu function $\mathrm{Fe}_{\nu}$
	modMathieuGe
		$\mathrm{Ge}_{\nu}\left(z,q\right)$	"	(28.20.7)	the modified Mathieu function $\mathrm{Ge}_{\nu}$
	modMathieuIe
		$\mathrm{Ie}_{n}\left(z,h\right)$	${\mathbb{Z}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(28.20.17)	the modified Mathieu function $\mathrm{Ie}_{n}$
	modMathieuIo
		$\mathrm{Io}_{n}\left(z,h\right)$	"	(28.20.18)	the modified Mathieu function $\mathrm{Io}_{n}$
	modMathieuKe
		$\mathrm{Ke}_{n}\left(z,h\right)$	"	(28.20.19)	the modified Mathieu function $\mathrm{Ke}_{n}$
	modMathieuKo
		$\mathrm{Ko}_{n}\left(z,h\right)$	"	(28.20.20)	the modified Mathieu function $\mathrm{Ko}_{n}$
	modMathieuM
		${\mathrm{M}^{(j)}_{\nu}}\left(z,h\right)$	${\mathbb{Z}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§28.20(iii)	the modified Mathieu function ${\mathrm{M}^{(j)}_{\nu}}$
	modMathieuMe
		$\mathrm{Me}_{\nu}\left(z,q\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(28.20.5)	the modified Mathieu function $\mathrm{Me}_{\nu}$
	modMathieuSe
		$\mathrm{Se}_{\nu}\left(z,q\right)$	"	(28.20.4)	the modified Mathieu function $\mathrm{Se}_{\nu}$
DLMF_MA_rad.ocd Mathieu Functions and Hill’s Equation – Radial
	radMathieuMc
		${\mathrm{Mc}^{(j)}_{n}}\left(z,h\right)$	${\mathbb{Z}\times\mathbb{Z}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(28.20.15)	the radial Mathieu function ${\mathrm{Mc}^{(j)}_{n}}$
	radMathieuMs
		${\mathrm{Ms}^{(j)}_{n}}\left(z,h\right)$	"	(28.20.16)	the radial Mathieu function ${\mathrm{Ms}^{(j)}_{n}}$
DLMF_NT.ocd Functions of Number Theory
	Eulertotientphi
		$\phi\left(n\right)$	${{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$	(27.2.7)	Euler’s totient, the number of positive integers relatively prime to $n$ , ( $\phi=\phi_{0}$ )
		$\phi_{k}\left(n\right)$	${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$	(27.2.6)	the sum of $k$ ^th powers of integers relatively prime to $n$
	JordanJ	$J_{k}\left(n\right)$	"	(27.2.11)	Jordan’s function
	Liouvillelambda
		$\lambda\left(n\right)$	${{\mathbb{Z}^{+}}\to\left\{0,\pm 1\right\}}$	(27.2.13)	the Liouville’s function
	Mangoldtlambda
		$\Lambda\left(n\right)$	${{\mathbb{Z}^{+}}\to\mathbb{R}}$	(27.2.14)	Mangoldt’s function
	Moebiusmu
		$\mu\left(n\right)$	${{\mathbb{Z}^{+}}\to\left\{0,\pm 1\right\}}$	(27.2.12)	the Möbius function
	ndivisors
		$d\left(n\right)$	${{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$	§27.2(i)	the number of divisors of $n$ (divisor function)
		$d_{k}\left(n\right)$	${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$		the number of ways of expressing $n$ as product of $k$ factors
	nprimes	$\pi\left(x\right)$	${\mathbb{R}\to{\mathbb{Z}^{*}}}$	(27.2.2)	the number of primes not exceeding $x$
	nprimesdiv
		$\nu\left(n\right)$	${{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$	§27.2(i)	the number of distinct primes dividing $n$
	sumdivisors
		$\sigma_{\alpha}\left(n\right)$	${\mathbb{C}\times{\mathbb{Z}^{+}}\to\mathbb{C}}$	(27.2.10)	the sum of powers of divisors of $n$
DLMF_NT_aux.ocd Functions of Number Theory – Auxiliary
	Dedikindeta
		$\eta\left(\tau\right)$	${\mathbb{C}\to\mathbb{C}}$	(27.14.12)	Dedekind’s eta function (or modular function)
	Dirichletchar
		$\chi\left(n,k\right)$	${{\mathbb{Z}^{*}}\to\left\{0,1\right\}}$	§27.8	the Dirichlet character
		$\chi_{r}\left(n,k\right)$
	DiscriminantDelta
		$\Delta\left(\tau\right)$	${\mathbb{C}\to\mathbb{C}}$	(27.14.16)	the discriminant function
	Eulerphi
		$\mathit{f}\left(x\right)$	${\mathbb{R}\to\mathbb{R}}$	(27.14.2)	Euler’s reciprocal function
	Gausssum
		$G\left(n,\chi\right)$	${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\to\mathbb{C}}$	(27.10.9)	the Gauss sum
	Jacobisym
		$(n\|p)$	${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\to\left\{0,\pm 1\right\}}$	§27.9	the Jacobi symbol
	Legendresym
		$(n\|p)$	"	§27.9	the Legendre symbol
	Ramanujantau
		$\tau\left(n\right)$	${{\mathbb{Z}^{+}}\to\mathbb{Z}}$	(27.14.18)	Ramanujan’s tau function
	Rmanujansum
		$c_{k}\left(n\right)$	${{\mathbb{Z}^{+}}\to\mathbb{R}}$	(27.10.4)	Ramanujan’s sum
	WaringG	$G\left(k\right)$	${{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$	§27.13(iii)	Waring’s function $G$
	Waringg	$g\left(k\right)$	"	"	Waring’s function $g$
	nsquares
		$r_{k}\left(n\right)$	${{\mathbb{Z}^{+}}\times{\mathbb{Z}^{+}}\to{\mathbb{Z}^{*}}}$	§27.13(iv)	the number of squares
DLMF_OP.ocd Orthogonal Polynomials
	ChebyshevpolyT
		$T_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.3	the Chebyshev polynomial of the first kind
	ChebyshevpolyU
		$U_{n}\left(x\right)$	"	§18.3	the Chebyshev polynomial of the second kind
	ChebyshevpolyV
		$V_{n}\left(x\right)$	"	§18.3	the Chebyshev polynomial of the third kind
	ChebyshevpolyW
		$W_{n}\left(x\right)$	"	§18.3	the Chebyshev polynomial of the fourth kind
	HermitepolyH
		$H_{n}\left(x\right)$	"	§18.3	the Hermite polynomial
	JacobipolyP
		$P^{(\alpha,\beta)}_{n}\left(x\right)$	${\mathbb{R}\times\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.3	the Jacobi polynomial
	LaguerrepolyL
		$L_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.1	$=L^{(0)}_{n}$ , shorthand for the Laguerre polynomial
		$L^{(\alpha)}_{n}\left(x\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.3	the (generalized or associated) Laguerre (or Sonin) polynomial
	LegendrepolyP
		$P_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.3	the Legendre (or spherical) polynomial
	dilChebyshevpolyC
		$C_{n}\left(x\right)$	"	(18.1.3)	the dilated Chebyshev polynomial of first kind
	dilChebyshevpolyS
		$S_{n}\left(x\right)$	"	"	the dilated Chebyshev polynomial of second kind
	dilHermitepolyHe
		$\mathit{He}_{n}\left(x\right)$	"	§18.3	the dilated Hermite polynomial
	shiftChebyshevpolyT
		$T^{*}_{n}\left(x\right)$	"	§18.3	the shifted Chebyshev polynomial of the first kind
	shiftChebyshevpolyU
		$U^{*}_{n}\left(x\right)$	"	§18.3	the shifted Chebyshev polynomial of the second kind
	shiftJacobipolyG
		$G_{n}\left(p,q,x\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times{\mathbb{Z}^{*}}\times\mathbb{R}% \to\mathbb{R}}$	(18.1.2)	the shifted Jacobi polynomial
	shiftLegendrepolyP
		$P^{*}_{n}\left(x\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.3	the shifted Legendre polynomial
	ultrasphpoly
		$C^{(\lambda)}_{n}\left(x\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\to\mathbb{R}}$	§18.3	the ultraspherical (or Gegenbauer) polynomial
DLMF_OP_askey.ocd Orthogonal Polynomials – askey
	CharlierpolyC
		$C_{n}\left(x;a\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	§18.19	the Charlier polynomial
	HahnpolyQ
		$Q_{n}\left(x;\alpha,\beta,N\right)$	${{\mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times{% \mathbb{Z}^{}}\to\mathbb{R}}$
				§18.19	the Hahn polynomial
	KrawtchoukpolyK
		$K_{n}\left(x;p,N\right)$	${{\mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\times{\mathbb{Z}^{}}\to% \mathbb{R}}$	§18.19	the Krawtchouk polynomial
	MeixnerPollaczekpolyP
		$P^{(\lambda)}_{n}\left(x;\phi\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	§18.19	the Meixner–Pollaczek polynomial
	MeixnerpolyM
		$M_{n}\left(x;\beta,c\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	§18.19	the Meixner polynomial
	RacahpolyR
		$R_{n}\left(x;\alpha,\beta,\gamma,\delta\right)$
			${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{C}\times\mathbb{C}\times\mathbb% {C}\times\mathbb{C}\to\mathbb{C}}$
				§18.25	the Racah polynomial
	WilsonpolyW
		$W_{n}\left(x;a,b,c,d\right)$
			"	§18.25	the Wilson polynomial
	contHahnpolyp
		$p_{n}\left(x;a,b,\overline{a},\overline{b}\right)$
			${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§18.19	the continuous Hahn polynomial
	contdualHahnpolyS
		$S_{n}\left(x;a,b,c\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{C}\times\mathbb{C}\times\mathbb% {C}\to\mathbb{C}}$	§18.25	the continuous dual Hahn polynomial
	dualHahnpolyR
		$R_{n}\left(x;\gamma,\delta,N\right)$	${{\mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times{% \mathbb{Z}^{}}\to\mathbb{C}}$
				§18.25	the dual Hahn polynomial
DLMF_OP_aux.ocd Orthogonal Polynomials – Auxiliary
	Besselpolyy
		$y_{n}\left(x;a\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.34.1)	the Bessel polynomial
	PollaczekpolyP
		$P^{(\lambda)}_{n}\left(x;a,b\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\to\mathbb{R}}$	(18.35.4)	the Pollaczek polynomial
	assJacobipolyP
		$P^{(\alpha,\beta)}_{n}\left(x;c\right)$	${\mathbb{R}\times\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb% {R}\to\mathbb{R}}$	(18.30.4)	the associated Jacobi polynomial
	assLegendrepoly
		$P_{n}\left(x;c\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.30.6)	the associated Legendre polynomial
	diskpoly
		$R^{(\alpha)}_{m,n}\left(z\right)$	${\mathbb{R}\times{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{C}\to% \mathbb{C}}$	(18.37.1)	the disk polynomial
	trianglepoly
		$P^{\alpha,\beta,\gamma}_{m,n}\left(x,y\right)$	${\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times{\mathbb{Z}^{}}\times{% \mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$
				(18.37.7)	the triangle polynomial
DLMF_OP_mat.ocd Orthogonal Polynomials – Matrix arguments
	JacobifunPmat
		$P^{(\gamma,\delta)}_{\nu}\left(\mathbf{T}\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times{\mathbb{C}}^{\bullet\times% \bullet}\to\mathbb{C}}$	(35.7.2)	the Jacobi function of matrix argument
	LaguerrefunLmat
		$L_{\nu}\left(\mathbf{T}\right)$	${\mathbb{C}\times\mathbb{C}\times{\mathbb{C}}^{\bullet\times\bullet}\to\mathbb% {C}}$	(35.6.3)	the Laguerre function of matrix argument
		$L^{(\gamma)}_{\nu}\left(\mathbf{T}\right)$
DLMF_OP_q.ocd Orthogonal Polynomials – $q$ -analogues
	AlSalamChiharapolyQ
		$Q_{n}\left(x;a,b\,\|\,q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\to\mathbb{R}}$	(18.28.7)	the Al-Salam–Chihara polynomial
	AskeyWilsonpolyp
		$p_{n}\left(x;a,b,c,d\,\|\,q\right)$
			${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$
				(18.28.1)	the Askey–Wilson polynomial
	StieltjesWigertpolyS
		$S_{n}\left(x;q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.27.18)	the Stieltjes–Wigert polynomial
	bigqJacobipolyP
		$P_{n}\left(x;a,b,c;q\right)$
			${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\times\mathbb{R}\to\mathbb{R}}$
				(18.27.5)	the big $q$ -Jacobi polynomial
	contqHermitepolyH
		$H_{n}\left(x\,\|\,q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.28.16)	the continuous $q$ -Hermite polynomial
	contqinvHermitepolyh
		$h_{n}\left(x\,\|\,q\right)$	"	(18.28.18)	the continuous $q^{-1}$ -Hermite polynomial
	contqultrasphpoly
		$C_{n}\left(x;\beta\,\|\,q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.28.13)	the continuous $q$ -ultraspherical (or Rogers) polynomial
	discqHermitepolyhI
		$h_{n}\left(x;q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.27.21)	the discrete $q$ -Hermite I polynomial
	discqHermitepolyhII
		$\tilde{h}_{n}\left(x;q\right)$	"	(18.27.23)	the discrete $q$ -Hermite II polynomial
	littleqJacobipolyp
		$p_{n}\left(x;a,b;q\right)$	${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\to\mathbb{R}}$	(18.27.13)	the little $q$ -Jacobi polynomial
	qHahnpolyQ
		$Q_{n}\left(x;\alpha,\beta,N;q\right)$
			${{\mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times{% \mathbb{Z}^{}}\times\mathbb{R}\to\mathbb{R}}$
				(18.27.3)	the $q$ -Hahn polynomial
	qLaguerrepolyL
		$L^{(\alpha)}_{n}\left(x;q\right)$	${\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$	(18.27.15)	the $q$ -Laguerre polynomial
	qRacahpolyR
		$R_{n}\left(x;\alpha,\beta,\gamma,\delta\,\|\,q\right)$
			${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$
				(18.28.19)	the $q$ -Racah polynomial
	qinvAlSalamChiharapolyQ
		$Q_{n}\left(x;a,b\,\|\,q^{-1}\right)$
			${{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb{R}\times\mathbb{R}\times\mathbb% {R}\to\mathbb{R}}$	(18.28.9)	the $q^{-1}$ -Al-Salam–Chihara polynomial
	scbigqJacobipolyP
		$P^{(\alpha,\beta)}_{n}\left(x;c,d;q\right)$
			${\mathbb{R}\times\mathbb{R}\times{\mathbb{Z}^{*}}\times\mathbb{R}\times\mathbb% {R}\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}}$
				(18.27.6)	the scaled big $q$ -Jacobi polynomial
DLMF_PC.ocd Parabolic Cylinder Functions
	WhittakerparaD
		$D_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§12.1	Whittaker’s notation for the parabolic cylinder function
	paraU	$U\left(a,z\right)$	"	§12.2(i)	the parabolic cylinder (or Weber) function $U$
	paraV	$V\left(a,z\right)$	"	"	the parabolic cylinder (or Weber) function $V$
	paraW	$W\left(a,z\right)$	"	§12.14(i)	the parabolic cylinder (or Weber) function $W$
DLMF_PC_mag.ocd Parabolic Cylinder Functions – Magnitudes, Phases
	envparaU
		$\mathrm{env}\mskip-1.0mu U\left(c,x\right)$	${\mathbb{C}\times\mathbb{R}\to\mathbb{R}}$	§14.15(v)	the envelope of the parabolic cylinder function $U$
	envparaUbar
		$\mathrm{env}\mskip-1.0mu \overline{U}\left(c,x\right)$	"	"	the envelope of the parabolic cylinder function $\overline{U}$
	paraUbar
		$\overline{U}\left(a,x\right)$	${\mathbb{C}\times\mathbb{R}\to\mathbb{C}}$	§12.2(vi)	the parabolic cylinder (or Weber) function $\overline{U}$
DLMF_ST.ocd Struve and Related Functions
	StruveH	$\mathbf{H}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(11.2.1)	the Struve function $\mathbf{H}_{\nu}$
	StruveK	$\mathbf{K}_{\nu}\left(z\right)$	"	(11.2.5)	the Struve function $\mathbf{K}_{\nu}$
DLMF_ST_aux.ocd Struve and Related Functions – Auxiliary
	AngerJ	$\mathbf{J}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(11.10.1)	the Anger function
	AngerWeberA
		$\mathbf{A}_{\nu}\left(z\right)$	"	(11.10.4)	the Anger–Weber function
	WeberE	$\mathbf{E}_{\nu}\left(z\right)$	"	(11.10.2)	the Weber function
DLMF_ST_lommel.ocd Struve and Related Functions – lommel
	LommelS	$S_{{\mu},{\nu}}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(11.9.5)	the Lommel function $S_{{\mu},{\nu}}$
	Lommels	$s_{{\mu},{\nu}}\left(z\right)$	"	(11.9.3)	the Lommel function $s_{{\mu},{\nu}}$
DLMF_ST_mod.ocd Struve and Related Functions – Modified
	modStruveL
		$\mathbf{L}_{\nu}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(11.2.2)	the modified Struve function $\mathbf{L}_{\nu}$
	modStruveM
		$\mathbf{M}_{\nu}\left(z\right)$	"	(11.2.6)	the modified Struve function $\mathbf{M}_{\nu}$
DLMF_SW.ocd Spheroidal Wave Functions
	radsphwaveS
		$S^{m(j)}_{n}\left(z,\gamma\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times{\mathbb{Z}^{*}}\times\mathbb{C}% \times\mathbb{R}\to\mathbb{C}}$
				(30.11.3)	the radial spheroidal wave function
	spheigvalLambda
		$\lambda^{m}_{n}\left(\gamma^{2}\right)$		§30.3(i)	the eigenvalues of the spheroidal differential equation
	sphwavePs
		$\mathit{Ps}^{m}_{n}\left(z,\gamma^{2}\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{C}\times\mathbb{R}\to% \mathbb{C}}$	§30.6	the spheroidal wave function of complex argument
	sphwaveQs
		$\mathit{Qs}^{m}_{n}\left(z,\gamma^{2}\right)$	"	"	"
DLMF_SW_real.ocd Spheroidal Wave Functions – Real
	sphwavePsreal
		$\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)$	${{\mathbb{Z}^{}}\times{\mathbb{Z}^{}}\times\mathbb{R}\times\mathbb{R}\to% \mathbb{R}}$	§30.4(i)	the spheroidal wave function of first kind
	sphwaveQsreal
		$\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right)$	"	§30.5	the spheroidal wave function of second kind
DLMF_TH.ocd Theta Functions
	Jacobithetacombinedq
		$\varphi_{n,m}\left(z,q\right)$	${\left\{1,2,3,4\right\}\times\left\{1,2,3,4\right\}\times\mathbb{C}\times% \mathbb{C}\to\mathbb{C}}$
				§20.11(v)	the combined theta function
	Jacobithetaq
		$\theta_{j}\left(z,q\right)$	${\left\{1,2,3,4\right\}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$
				§20.2(i)	the Jacobi theta function of $q$
	Jacobithetatau
		$\theta_{j}\left(z\middle\|\tau\right)$	"	"	the Jacobi theta function of $\tau$
DLMF_TH_Riemann.ocd Theta Functions – Riemann
	Riemanntheta
		$\theta\left(z\middle\|\Omega\right)$	${\mathbb{C}\times{\mathbb{C}}^{\bullet\times\bullet}\to\mathbb{C}}$	(21.2.1)	the Riemann theta function
	Riemannthetachar
		$\theta\genfrac{[}{]}{0.0pt}{}{\alpha}{\beta}\left(z\middle\|\Omega\right)$	${{\mathbb{R}}^{\bullet}\times{\mathbb{R}}^{\bullet}\times\mathbb{C}\times{% \mathbb{C}}^{\bullet\times\bullet}\to\mathbb{C}}$
				(21.2.5)	the Riemann theta function with characteristics
	scRiemanntheta
		$\hat{\theta}\left(z\middle\|\Omega\right)$	${\mathbb{C}\times{\mathbb{C}}^{\bullet\times\bullet}\to\mathbb{C}}$	(21.2.2)	the scaled Riemann theta function (or oscillatory part of the theta function)
DLMF_TJ.ocd 3 extitj, 6 extitj, 9 extitj Symbols
	Wignerninejsym
		$\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}$	${(\mathbb{Z}/2)^{9}}$	(34.6.1)	the Wigner $9j$ symbol
	Wignersixjsym
		$\begin{Bmatrix}j_{1}&j_{2}&j_{3}\\ l_{1}&l_{2}&l_{3}\end{Bmatrix}$	${(\mathbb{Z}/2)^{6}}$	(34.4.1)	the Wigner $6j$ symbol
	Wignerthreejsym
		$\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&m_{3}\end{pmatrix}$	"	(34.2.4)	the Wigner $3j$ symbol
DLMF_WE.ocd Weierstrass Elliptic and Modular Functions
	KleincompinvarJtau
		$J\left(\tau\right)$	${\mathbb{C}\to\mathbb{C}}$	(23.15.7)	Klein’s complete invariant
	modularlambdatau
		$\lambda\left(\tau\right)$	"	(23.15.6)	the elliptic modular function
DLMF_WE_invar.ocd Weierstrass Elliptic and Modular Functions – on invariants
	Weierstrasspinvar
		$\wp\left(z;g_{2},g_{3}\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(23.3.8)	the Weierstrass $\wp$ -function (on invariants)
	Weierstrasssigmainvar
		$\sigma\left(z;g_{2},g_{3}\right)$	"	§23.3(i)	the Weierstrass sigma function $\sigma$ (on invariants)
	Weierstrasszetainvar
		$\zeta\left(z;g_{2},g_{3}\right)$	"	"	the Weierstrass zeta function $\zeta$ (on invariants)
DLMF_WE_lattice.ocd Weierstrass Elliptic and Modular Functions – on Lattice
	Weierstrasselatt
		$e_{i}\left(L\right)$	${\mathbf{L}\to\mathbb{C}}$	§23.3(i)	the Weierstrass lattice roots (on Lattice)
	Weierstrassinvarlatt
		$g_{i}\left(L\right)$	"	§23.3	the Weierstrass invariants (on Lattice)
	Weierstrassplatt
		$\wp\left(z\|L\right)$	${\mathbb{C}\times\mathbf{L}\to\mathbb{C}}$	(23.2.4)	the Weierstrass $\wp$ -function (on Lattice)
	Weierstrasssigmalatt
		$\sigma\left(z\|L\right)$	"	(23.2.6)	the Weierstrass sigma function $\sigma$ (on Lattice)
	Weierstrasszetalatt
		$\zeta\left(z\|L\right)$	"	(23.2.5)	the Weierstrass zeta function $\zeta$ (on Lattice)
DLMF_ZE.ocd Zeta and Related Functions
	ChebyshevPsi
		$\psi\left(x\right)$	${\mathbb{C}\to\mathbb{C}}$	(25.16.1)	the Chebyshev $\psi$ -function
	DirichletL
		$L\left(s,\chi\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(25.15.1)	the Dirichlet $L$ -function
	EulersumH
		$H\left(s\right)$	${\mathbb{C}\to\mathbb{C}}$	§25.16(ii)	the Euler sum
	Hurwitzzeta
		$\zeta\left(s,a\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(25.11.1)	the Hurwitz zeta function
	Jonquierephi
		$\phi\left(z,s\right)$	"	§25.12(ii)	Truesdell’s notation for polylogarithm
	LerchPhi
		$\Phi\left(z,s,a\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(25.14.1)	Lerch’s transcendent
	Riemannxi
		$\xi\left(s\right)$	${\mathbb{C}\to\mathbb{C}}$	(25.4.4)	the Riemann $\xi$ function
	Riemannzeta
		$\zeta\left(s\right)$	"	(25.2.1)	the Riemann zeta function
	dilog	$\mathrm{Li}_{2}\left(z\right)$	"	(25.12.1)	the dilogarithm
	genEulersumH
		$H\left(s,z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§25.16(ii)	the generalized Euler sum
	perZeta	$F\left(x,s\right)$	${\mathbb{R}\times\mathbb{C}\to\mathbb{C}}$	(25.13.1)	the periodic zeta function
	polylog	$\mathrm{Li}_{s}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	(25.12.10)	the polylogarithm
DLMF_types.ocd
	UnitDisc
		$\mathbb{D}$		Intro.	the set of complex numbers in the (open) unit disc
arith1.ocd (official)
	abs	$\left\|x\right\|$		?	the absolute value of $x$
asymp1.ocd (experimental)
	O	$O\left(x\right)$		(2.1.3)	the order not exceeding
	asymptotic
		$\sim$		(2.1.1)	asymptotically equal
	o	$o\left(x\right)$		(2.1.2)	the order less than
asymp2.ocd (DLMF speculative)
	asymptotic_expansion
		$\sim$		§2.1(iii)	asymptotic expansion (the right-hand side is the asymptotic expansion of the left-hand side)
complex1.ocd (official)
	argument
		$\operatorname{ph}\left(z\right)$		(1.9.7)	the phase of a complex number $z$
	conjugate
		$\overline{z}$		(1.9.11)	the complex conjugate of a complex number $z$
	imaginary
		$\Im\left(z\right)$		(1.9.2)	the imaginary part of a complex number $z$
	real	$\Re\left(z\right)$		"	the real part of a complex number $z$
equals.ocd
	definition
		$\equiv$		Intro.	equal by definition
equivalence.ocd
	equivalence
		$\equiv$		Intro.	modular equivalence
integer2.ocd (experimental)
	divides	$\mathbin{\|}$		?	the divides operator operator
linalg1.ocd (official)
	scalarproduct
		$\cdot$		?	the vector dot product operator
	transpose
		$\mathbf{X}^{\mathrm{T}}$		"	the transpose of a matrix
	vectorproduct
		$\times$		"	the vector cross product operator
nums1.ocd (official)
	e	$\mathrm{e}$		(4.2.11)	the exponential base
	gamma	$\gamma$		(5.2.3)	the Euler constant
	i	$\mathrm{i}$		?	the imaginary unit
	pi	$\pi$		(3.12.1)	the ratio of the circumference of a circle to its diameter
physical_consts1.ocd (experimental)
	Boltzmann_constant
		$k$		CODATA	the Boltzmann constant
	speed_of_light
		$c$		CODATA	the speed of light
rounding1.ocd (official)
	ceiling	$\left\lceil x\right\rceil$		Intro.	the ceiling of a real number $x$
	floor	$\left\lfloor x\right\rfloor$		"	the floor of a real number $x$
set1.ocd (official)
	size	$\left\|x\right\|$		§26.1	the cardinality of a set
setname1.ocd (official)
	C	$\mathbb{C}$		Intro.	the set of complex numbers
	N	$\mathbb{N}$		"	the set of ‘natural’ numbers (positive integers)
	Q	$\mathbb{Q}$		"	the set of rational numbers
	R	$\mathbb{R}$		"	the set of real numbers
	Z	$\mathbb{Z}$		"	the set of integers
transc1.ocd (official)
	cos	$\operatorname{cos}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(4.14.2)	the cosine function
	cosh	$\operatorname{cosh}\left(z\right)$	"	(4.28.2)	the hyperbolic cosine function
	cot	$\operatorname{cot}\left(z\right)$	"	(4.14.7)	the cotangent function
	coth	$\operatorname{coth}\left(z\right)$	"	(4.28.7)	the hyperbolic cotangent function
	csc	$\operatorname{csc}\left(z\right)$	"	(4.14.5)	the cosecant function
	csch	$\operatorname{csch}\left(z\right)$	"	(4.28.5)	the hyperbolic cosecant function
	exp	$\operatorname{exp}\left(z\right)$	"	(4.2.19)	the exponential function
	ln	$\operatorname{ln}\left(z\right)$	"	(4.2.2)	the principal branch of logarithm function
	log	$\operatorname{log}_{a}\left(z\right)$	${\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§4.2	the logarithm to general base $a$
	sec	$\operatorname{sec}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	(4.14.6)	the secant function
	sech	$\operatorname{sech}\left(z\right)$	"	(4.28.6)	the hyperbolic secant function
	sin	$\operatorname{sin}\left(z\right)$	"	(4.14.1)	the sine function
	sinh	$\operatorname{sinh}\left(z\right)$	"	(4.28.1)	the hyperbolic sine function
	tan	$\operatorname{tan}\left(z\right)$	"	(4.14.4)	the tangent function
	tanh	$\operatorname{tanh}\left(z\right)$	"	(4.28.4)	the hyperbolic tangent function
veccalc1.ocd (official)
	curl	$\operatorname{curl}$		(1.6.22)	the curl operator
	divergence
		$\operatorname{div}$		(1.6.21)	the divergence operator
	grad	$\operatorname{grad}$		(1.6.20)	the gradient operator
Unclassified
	AGM	$M\left(a,g\right)$		§19.8(i)	arithmetic-geometric mean
	Bohrradius
		$a_{0}$		CODATA	the Bohr radius
	Diracdelta
		$\delta\left(x\right)$		§1.17(i)	the Dirac delta functional (or distribution)
	Diracdeltaseq
		$\delta_{n}\left(x\right)$		"	the Dirac delta sequence
	FiniteSet
		$\left\{x_{0},\ldots\right\}$		?	elements of the finite set
	Fouriercostrans
		$\mathscr{F}_{\mskip-3.0mu c}\left(f\right)$		(1.14.9)	the Fourier cosine transform of a function
	Fouriersintrans
		$\mathscr{F}_{\mskip-2.0mu s}\left(f\right)$		(1.14.10)	the Fourier sine transform of a function
	Fouriertrans
		$\mathscr{F}\left(f\right)$		(1.14.1)	the Fourier transform of a function
	Fouriertransdist
		$\mathscr{F}\left(f\right)$		(1.16.35)	the Fourier transform of a distribution
	HeavisideH
		$H\left(x\right)$		(1.16.13)	the Heaviside function
	Hilberttrans
		$\mathcal{H}\left(f\right)$		§1.14(v)	the Hilbert transform of a function
	Kroneckerdelta
		$\delta_{j,k}$		Intro.	the Kronecker delta
	Laplacetrans
		$\mathscr{L}\left(f\right)$		(1.14.17)	the Laplace transform of a function
	Lattices
		$\mathbf{L}$		?	the set of Lattices on the complex plane (in the sense of elliptic functions)
	LauricellaFD ( $\lx@stackrel{{\scriptstyle?}}{{\equiv}}$ hypergeon2:LauricellaFD)
		$F_{D}\left(x;y;z;p\right)$	${\mathbb{C}\times\mathbb{C}\times\mathbb{C}\times\mathbb{C}\to\mathbb{C}}$	§19.15	Lauricella’s (multivariate) hypergeometric function
	Matrices
		${T}^{\bullet\times\bullet}\left(T\right)$		?	Matrices with elements of the given type; dimensions $n\times m$
		${T}^{n\times\ m}\left(T\right)$
	Mellintrans
		$\mathscr{M}\left(f\right)$		(1.14.32)	the Mellin transform of a function
	Pade	${[p/q]_{f}}\left(z\right)$		§3.11(iv)	the Padé approximant
	Rydbergconst
		$R_{\infty}$		CODATA	the Rydberg constant
	Schwarzian
		$\left\{z,\zeta\right\}$		(1.13.20)	the Schwarzian
	Stieltjestrans
		$\mathcal{S}\left(f\right)$		(1.14.47)	the Stieltjes transform of a function
	Tuples	${T}^{\bullet}$		?	$n$ -Tuples of elements of type $T$
		${T}^{n}$
	Vectors	${T}^{\bullet}\left(T\right)$		"	Vectors with elements of type $T$ ; dimension $n$
		${T}^{n}\left(T\right)$
	Wronskian
		$\mathscr{W}\left\{w_{1},w_{2}\right\}$		(1.13.4)	the Wronskian
	cartprod
		$\times$		§23.1	the Cartesian product operator
	continuous[]
		$C(a,b)$		§1.4(ii)	the set of functions continuous on the interval $(a,b)$
	continuous
		$C^{n}(a,b)$		§1.4	the set of continuous functions $n$ -times differentiable on the interval $(a,b)$
	diag	$\operatorname{diag}$		?	the diagonal elements
	diffd	$\mathrm{d}$		"	the differential operator
	electricconst
		$\varepsilon_{0}$		CODATA	the electric constant or vacuum permitivity
	env	$\operatorname{env}f$		?	the envelope of a function
	exptrace
		$\mathrm{etr}\left(\mathbf{X}\right)$		§35.1	the exponential of the trace
	finestructureconst
		$\alpha$		CODATA	the fine-structure constant
	intinnerprod
		$\left\langle\Lambda,\phi\right\rangle$		§1.16(i)	the inner-product (by integration)
	log	$\operatorname{log}\left(z\right)$	${\mathbb{C}\to\mathbb{C}}$	§4.2	the logarithm to base 10
	nonnegIntegers
		${\mathbb{Z}^{*}}$		?	the set of non-negative integers
	pgcd	$\left(a_{1},\ldots,a_{n}\right)$		§27.1	the greatest common divisor
	posIntegers
		${\mathbb{Z}^{+}}$		?	the set of positive integers
	setmod	$/$		§21.1	the set modulus operator
	shiftfactorial
		${\left[a\right]_{k}}$		(35.4.1)	the partitional shifted factorial
	sign	$\operatorname{sign}\left(x\right)$		Intro.	the sign of a number $x$
	trace	$\operatorname{tr}$		"	the trace of a matrix
	variation[]
		$\mathcal{V}\left(f\right)$		(1.4.33)	the total variation of a function
	variation
		$\mathcal{V}_{a,b}\left(f\right)$			the total variation of a function on an interval
	zonalpolyZ
		$Z_{\kappa}\left(\mathbf{T}\right)$		§35.4(i)	the zonal polynomial