Hypergeom2F1: Gauss hypergeometric function 2F1(a,b,c,z)

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Gauss hypergeometric function 2F1(a,b,c,z)

Description

Hypergeom2F1(a, b, c, z) computes the Gauss hypergeometric function 2F1(a,b,c,z), for the real parameters a, b and c (here assumed to be scalars), and the complex argument z (could be scalar, vector or array).

Usage

Hypergeom2F1(a, b, c, z)

Arguments

a	parameter - real scalar.
b	parameter - real scalar.
c	parameter - real scalar.
z	complex argument - scalar, vector or array.

Details

The functions based on Hypergeom2F1 is badly conditioned for when c is negative integer. In such situations, approximate the function value by using the noninteger parameter c, say c = c + eps, for some small eps.

Value

The Gauss hypergeometric function 2F1(a,b,c,z).

Note

Ver.: 06-Oct-2018 18:36:05 (consistent with Matlab CharFunTool v1.3.0, 18-Aug-2018 18:32:27).

References

The algorithm is based on a Fortran program in

S. Zhang & J. Jin "Computation of Special Functions" (Wiley, 1996). Converted by Ben Barrowes ([e-mail]).

See Also

Other Utility Function: ChebCoefficients(), ChebPoints(), ChebPolyValues(), ChebPoly(), ChebValues(), GammaLog(), GammaMultiLog(), GammaMulti(), GammaZX(), Hypergeom1F1MatApprox(), Hypergeom1F1Mat(), Hypergeom2F1Mat(), HypergeompFqMat(), InterpChebValues(), hypergeom1F1(), interpBarycentric()

Examples

## EXAMPLE 1
a <- 3
b <- 2.5
c <- 1.5
z <- 1i * seq(0, 1, by = 0.05)
f <- Hypergeom2F1(a, b, c, z)

# EXAMPLE 2
t <- 1i * seq(-5, 5, length.out = 11)
a <- 3 * t
b <- 2.5 * t
c <- 1.5 * t
z <- 0.75
f <- Hypergeom2F1(a,b,c,z)

gajdosandrej/CharFunToolR documentation built on June 3, 2024, 7:46 p.m.