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2 Naming conventions

Briefly, the names of the various mathematical function macros are derived from the descriptive ‘Proper Name’ of the function according to:

𝑚𝑎𝑐𝑟𝑜\𝑝𝑟𝑒𝑓𝑖𝑥*𝑛𝑎𝑚𝑒𝑐𝑙𝑎𝑠𝑠?𝑠𝑦𝑚𝑏𝑜𝑙?𝑠𝑢𝑓𝑓𝑖𝑥*

The 𝑛𝑎𝑚𝑒 is the ‘conventional’ name or based on the “inventor’s” name. The 𝑐𝑙𝑎𝑠𝑠 indicates function (generally omitted), integrals, polynomials, and so on. The 𝑠𝑦𝑚𝑏𝑜𝑙 is the latinized form of the notation, upper or lower case as appropriate. The 𝑝𝑟𝑒𝑓𝑖𝑥 modifier includes all significant characteristics that may distinguish functions (eg. ‘modified Bessel’ vs. simply ‘Bessel’). The 𝑠𝑢𝑓𝑓𝑖𝑥 generally indicates limitations or special cases regarding arguments. The 𝑝𝑟𝑒𝑓𝑖𝑥, 𝑐𝑙𝑎𝑠𝑠 and 𝑠𝑢𝑓𝑓𝑖𝑥 are abbreviated for brevity, given in Table 4. For predicability, we avoid abbreviating people’s names.

Table 2: Function classes for macros
𝑐𝑙𝑎𝑠𝑠 Meaning
function (omitted by default)
char characteristic
eigval eigenvalues
eigvec eigenvectors
int integral
mod modulus
number number
phase phase (or phase shift)
poly polynomial
sum sum
sym symbol
trans transform
wave wavefunction
Table 3: Suffix abbreviations
𝑠𝑢𝑓𝑓𝑖𝑥 Meaning
imag imaginary argument or order
k elliptic functions of k, modulus
m elliptic functions of parameter m=k2
mat matrix argument
real real argument or order
invar on invariants (Weierstrass)
latt on lattice (Weierstrass)
q functions of q, nome
tau functions of τ
Table 4: Abbreviations for macro 𝑝𝑟𝑒𝑓𝑖𝑥’s
𝑝𝑟𝑒𝑓𝑖𝑥 Meaning
a arc, inverse (circular functions)
A arc, multi-valued-inverse
aff affine
ass associated
aux auxilliary
big big
canon canonical
comp complete
ccomp complete complementary
cont continuous
cusp cuspoid
deriv derivative(s) of
diff differential
diffr diffraction
dil dilated
disc discrete
div dividing
dual dual
ell elliptic
env envelope of
exp exponential
gen general | generalized
hyper hyperbolic | hypergeometric
inc incomplete
inv inverse
irreg irregular
little little
log logarithm(ic)
mod modified (or modular?)
multivar multivariate
n number of
norm normalized or normalization
para parabolic
per periodic
q q-variant of
rad radial
reg regular
rest restricted
sc scaled
shift shifted
sph spherical | spheroidal
sym symmetric
umb umbilic
usph ultraspherical
z zeros (of)