Subsections

• 5.7.1 Real $z$ and Integer or Half-Integer $p$
• 5.7.2 Real $z$ and Real $p$
• 5.7.3 Complex $z$ and Real or Complex $p$
• 5.7.4 Inverse Function
• 5.7.5 Articles

5.7 Incomplete Gamma Functions, Generalized Exponential Integrals

These functions are essentially equivalent; thus $E_p (z) = z^{p-1} \Gamma (1-p,z).$ This section includes the chi-square distribution function.

5.7.1 Real $z$ and Integer or Half-Integer $p$

[Amo80a, Fortran], [FO94], [SP75, Fortran], [SZ74, Fortran]. Libraries: [Mos89], [Tho97], [ULI90], [ZJ96], IMSL, SLATEC. Systems: Maple.

5.7.2 Real $z$ and Real $p$

[CLM90a, Fortran], [CLM90b, Fortran], [DM87, Fortran], [Ful72, Fortran], [Gau79a, Fortran], [Moo82, Fortran], [She88, Fortran], [Tem94b, Pascal]. Libraries: [Bak92], [Mos89], [Tho97], [ULI90], [WNO94], [ZJ96], IMSL, NAG, Numerical Recipes, SLATEC. Systems: Maple.

5.7.3 Complex $z$ and Real or Complex $p$

Systems: Maple, Mathematica.

5.7.4 Inverse Function

[DM87, Fortran], [Phi88, Fortran]. Libraries: [Mos89], [ULI90], IMSL, NAG. Systems: Maple, Mathematica.

5.7.5 Articles

[AB87a], [Amo80b], [Bar61], [CLM87], [CLM88], [CLM90c], [P98], [DM86], [Gau79b], [Gau99], [JT85], [LDP93], [Luk75], [Mar82], [Tem85], [Tem87], [Tem92a], [Tem94a], [Tem95].