hypergeom - Maple Help

MTM

 hypergeom
 generalized hypergeometric function

 Calling Sequence hypergeom(N, D, z)

Parameters

 N - vector or scalar D - vector or scalar z - expression

Description

 • The hypergeom(N, D, z) calling sequence computes the generalized hypergeometric function F(n, d, z). Let N = [n1, n2, ...], j = length(N), D = [d1, d2, ...] and k = length(D).  This function is frequently denoted by jFk(n,d,z).
 • Formally, F(n, d, z) is defined by the series

$\sum _{k=0}^{\mathrm{\infty }}\frac{{z}^{k}\left(\prod _{i=1}^{p}\mathrm{pochhammer}\left({n}_{i},k\right)\right)}{k!\left(\prod _{j=1}^{q}\mathrm{pochhammer}\left({d}_{j},k\right)\right)}$

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $\mathrm{hypergeom}\left(\left[\right],\left[\right],z\right)$
 ${{ⅇ}}^{{z}}$ (1)
 > $\mathrm{hypergeom}\left(1,\left[\right],z\right)$
 ${-}\frac{{1}}{{-}{1}{+}{z}}$ (2)
 > $\mathrm{hypergeom}\left(1,2,z\right)$
 $\frac{{{ⅇ}}^{{z}}{}\left({1}{-}{{ⅇ}}^{{-}{z}}\right)}{{z}}$ (3)
 > $\mathrm{hypergeom}\left(\left[1,2\right],\left[2,3\right],z\right)$
 $\frac{{2}{}{{ⅇ}}^{{z}}{}\left({1}{-}{{ⅇ}}^{{-}{z}}{}\left({1}{+}{z}\right)\right)}{{{z}}^{{2}}}$ (4)
 > $\mathrm{hypergeom}\left(a,\left[\right],z\right)$
 ${\left({1}{-}{z}\right)}^{{-}{a}}$ (5)
 > $\mathrm{hypergeom}\left(\left[\right],1,-\frac{{z}^{2}}{4}\right)$
 ${\mathrm{BesselJ}}{}\left({0}{,}{z}\right)$ (6)
 > $\mathrm{hypergeom}\left(\left[-10,10\right],\frac{1}{2},\frac{1-z}{2}\right)$
 ${512}{}{{z}}^{{10}}{-}{1280}{}{{z}}^{{8}}{+}{1120}{}{{z}}^{{6}}{-}{400}{}{{z}}^{{4}}{+}{50}{}{{z}}^{{2}}{-}{1}$ (7)