# Hyperg: Hypergeometric functions In gsl: Wrapper for the Gnu Scientific Library

 Hyperg R Documentation

## Hypergeometric functions

### Description

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`

### 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).

There is a known issue in `hyperg_2F1()` in GSL-2.6, https://savannah.gnu.org/bugs/?54998 and the package returns the erroneous value given by GSL.

### Author(s)

Robin K. S. Hankin

### References

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

### Examples

```
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)
```

gsl documentation built on Feb. 16, 2023, 10:32 p.m.