The Hypergeometric Function

For more information on the Hypergeometric Series, see Husemöller [Hus87], page 176.

HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
Return the hypergeometric series F(a, b, c;z) defined by F(a, b, c;z) = ∑0≤n (((a)n(b)n)/(n!(c)n) zn) where (a)n = a (a + 1) ... (a + n - 1).
HypergeometricU(a, b, s) : FldReElt, FldReElt, FldReElt -> FldReElt
For positive real s and complex arguments a and b this function returns the value of the confluent hypergeometric function U(a, b, s). This can be defined by U(a, b, s)=(1/Γ(a))intu=0^∞e - suua - 1(1 + u)b - a - 1)du. Pari is used here.
V2.28, 13 July 2023