Hypergeometric functions are described in Abramowitz & Stegun, Chapters 13 and 15.
This routine computes the hypergeometric function \({}_0F_1(c,x)\).
This routine computes the confluent hypergeometric function \({}_1F_1(m,n,x) = M(m,n,x)\) for integer parameters \(m\), \(n\).
This routine computes the confluent hypergeometric function \({}_1F_1(a,b,x) = M(a,b,x)\) for general parameters \(a\), \(b\).
This routine computes the confluent hypergeometric function \(U(m,n,x)\) for integer parameters \(m\), \(n\).
This routine computes the confluent hypergeometric function \(U(a,b,x)\).
This routine computes the Gauss hypergeometric function \({}_2F_1(a,b,c,x) = F(a,b,c,x)\) for \(|x| < 1\).
If the arguments \((a,b,c,x)\) are too close to a singularity then the function can return an error when the series approximation converges too slowly. This occurs in the region of \(x=1, c - a - b = m\) for integer \(m\).
This routine computes the Gauss hypergeometric function \({}_2F_1(a_R + i a_I, a_R - i a_I, c, x)\) with complex parameters for \(|x| < 1\).
This routine computes the renormalized Gauss hypergeometric function \({}_2F_1(a,b,c,x) / \Gamma(c)\) for \(|x| < 1\).
This routine computes the renormalized Gauss hypergeometric function \({}_2F_1(a_R + i a_I, a_R - i a_I, c, x) / \Gamma(c)\) for \(|x| < 1\).
This routine computes the hypergeometric function \({}_2F_0(a,b,x)\). The series representation is a divergent hypergeometric series. However, for \(x < 0\) we have \({}_2F_0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)\)