Hyperg

0th

Percentile

Hypergeometric functions

Hypergeometric functions as per the Gnu Scientific Library reference manual section 7.21 and AMS-55, chapters 13 and 15. These functions are declared in header file gsl_sf_hyperg.h

Keywords
array
Usage
hyperg_0F1(c, x, give=FALSE, strict=TRUE)
hyperg_1F1_int(m, n, x, give=FALSE, strict=TRUE)
hyperg_1F1(a, b, x, give=FALSE, strict=TRUE)
hyperg_U_int(m, n, x, give=FALSE, strict=TRUE)
hyperg_U(a, b, x, give=FALSE, strict=TRUE)
hyperg_2F1(a, b, c, x, give=FALSE, strict=TRUE)
hyperg_2F1_conj(aR, aI, c, x, give=FALSE, strict=TRUE)
hyperg_2F1_renorm(a, b, c, x, give=FALSE, strict=TRUE)
hyperg_2F1_conj_renorm(aR, aI, c, x, give=FALSE, strict=TRUE)
hyperg_2F0(a, b, x, give=FALSE, strict=TRUE)
Arguments
x

input: real values

a,b,c

input: real values

m,n

input: integer values

aR,aI

input: real values

give

Boolean with TRUE meaning to return a list of three items: the value, an estimate of the error, and a status number.

strict

Boolean, with TRUE meaning to return NaN if status is an error

Note

“The circle of convergence of the Gauss hypergeometric series is the unit circle \(|z|=1\)” (AMS, page 556).

References

http://www.gnu.org/software/gsl

Aliases
  • Hyperg
  • hyperg
  • hyperg_0F1
  • hyperg_1F1_int
  • hyperg_1F1
  • hyperg_U_int
  • hyperg_U
  • hyperg_2F1
  • hyperg_2F1_conj
  • hyperg_2F1_renorm
  • hyperg_2F1_conj_renorm
  • hyperg_2F0
Examples
# NOT RUN {
hyperg_0F1(0.1,0.55)

hyperg_1F1_int(2,3,0.555)
hyperg_1F1(2.12312,3.12313,0.555)
hyperg_U_int(2, 3, 0.555)
hyperg_U(2.234, 3.234, 0.555)
# }
Documentation reproduced from package gsl, version 2.1-6, License: GPL-3

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