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) = sum_(0 <= n) (((a)_n(b)_n)/(n!(c)_n) z^n) where (a)_n = a (a + 1) ... (a + n - 1).

HypergeometricU(a, b, s) : FldPrElt, FldPrElt, FldPrElt -> FldPrElt

For positive free real s and free 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/Gamma(a))int_(u=0)^Infinity e^(-su)u^(a - 1)(1 + u)^(b - a - 1))du.