Hyperg function

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

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

References

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

Author(s)

Robin K. S. Hankin

Note

The circle of convergence of the Gauss hypergeometric series is theunit 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.

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)