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))int_u=0^∞e ^{- su}u^{a - 1}(1 + u)^{b - a - 1)}du. Pari is used here.