Module rgsl::hypergeometric [−] [src]

Hypergeometric functions are described in Abramowitz & Stegun, Chapters 13 and 15.

Functions

hyperg_0F1	This routine computes the hypergeometric function 0F1(c,x).
hyperg_0F1_e	This routine computes the hypergeometric function 0F1(c,x).
hyperg_1F1	This routine computes the confluent hypergeometric function 1F1(a,b,x) = M(a,b,x) for general parameters a, b.
hyperg_1F1_U_int	This routine computes the confluent hypergeometric function U(m,n,x) for integer parameters m, n.
hyperg_1F1_U_int_e	This routine computes the confluent hypergeometric function U(m,n,x) for integer parameters m, n.
hyperg_1F1_U_int_e10_e	This routine computes the confluent hypergeometric function U(m,n,x) for integer parameters m, n using the [`ResultE10]`(types/result/struct.ResultE10.html) type to return a result with extended range.
hyperg_1F1_e	This routine computes the confluent hypergeometric function 1F1(a,b,x) = M(a,b,x) for general parameters a, b.
hyperg_1F1_int	This routine computes the confluent hypergeometric function 1F1(m,n,x) = M(m,n,x) for integer parameters m, n.
hyperg_1F1_int_e	This routine computes the confluent hypergeometric function 1F1(m,n,x) = M(m,n,x) for integer parameters m, n.
hyperg_2F0	This routine computes the hypergeometric function 2F0(a,b,x). The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)
hyperg_2F1	This routine computes the Gauss hypergeometric function 2F1(a,b,c,x) = F(a,b,c,x) for \|x\| < 1.
hyperg_2F0_e	This routine computes the hypergeometric function 2F0(a,b,x). The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)
hyperg_2F1_conj	This routine computes the Gauss hypergeometric function 2F1(a_R + i a_I, a_R - i a_I, c, x) with complex parameters for \|x\| < 1.
hyperg_2F1_conj_e	This routine computes the Gauss hypergeometric function 2F1(a_R + i a_I, a_R - i a_I, c, x) with complex parameters for \|x\| < 1.
hyperg_2F1_conj_renorm	This routine computes the renormalized Gauss hypergeometric function 2F1(a_R + i a_I, a_R - i a_I, c, x) / \Gamma(c) for \|x\| < 1.
hyperg_2F1_conj_renorm_e	This routine computes the renormalized Gauss hypergeometric function 2F1(a_R + i a_I, a_R - i a_I, c, x) / \Gamma(c) for \|x\| < 1.
hyperg_2F1_e	This routine computes the Gauss hypergeometric function 2F1(a,b,c,x) = F(a,b,c,x) for \|x\| < 1.
hyperg_2F1_renorm	This routine computes the renormalized Gauss hypergeometric function 2F1(a,b,c,x) / \Gamma(c) for \|x\| < 1.
hyperg_2F1_renorm_e	This routine computes the renormalized Gauss hypergeometric function 2F1(a,b,c,x) / \Gamma(c) for \|x\| < 1.
hyperg_U	This routine computes the confluent hypergeometric function U(a,b,x).
hyperg_U_e	This routine computes the confluent hypergeometric function U(a,b,x).
hyperg_U_e10_e	This routine computes the confluent hypergeometric function U(a,b,x) using the [`ResultE10]`(types/result/struct.ResultE10.html) type to return a result with extended range.