hypergeom1F1: Confluent hypergeometric function

In Simkova/CharFun: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Description

HYPERGEOM1F1 Computes the confluent hypergeometric function 1F1(a,b,z), also known as the Kummer function M(a,b,z), for the real parameters a and b (here assumed to be scalars), and the complex argument z (could be scalar, vector or array).

Usage

hypergeom1F1(z, a, b)

Arguments

z	numerical values (number, vector...)
a	single value
b	single value

Details

The algorithm is based on a Fortran program in S. Zhang & J. Jin "Computation of Special Functions" (Wiley, 1996). Converted to matlab by using f2matlab: https://sourceforge.net/projects/f2matlab/ written by Ben Barrowes ([e-mail]).

Value

hypergeometric function 1F1(a,b,z)

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Confluent_hypergeometric_function

Examples

## EXAMPLE1 (CF of Beta(1/2,1/2) distribution)
a  = 1 / 2
b  = 1 / 2
t  = seq(-50, 50, length.out = 2 ^ 11)
plotGraf(function(t)
  hypergeom1F1(1i * t, a, b + b), t,
  title = "CF of the Beta distribution with alpha = 1/2, beta = 1/2")

Simkova/CharFun documentation built on May 9, 2019, 1:30 p.m.