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

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$\mathrm{hypergeom}\left(\left[\right]\,\left[\right]\,z\right)$

${\ⅇ}^z$

$\mathrm{hypergeom}\left(1\,\left[\right]\,z\right)$

$\frac{1}{1-z}$

$\mathrm{hypergeom}\left(1\,2\,z\right)$

$\frac{{\ⅇ}^z\left(1-{\ⅇ}^{-z}\right)}{z}$

$\mathrm{hypergeom}\left(\left[1\,2\right]\,\left[2\,3\right]\,z\right)$

$\frac{2{\ⅇ}^z\left(1-{\ⅇ}^{-z}\left(1+z\right)\right)}{z^2}$

$\mathrm{hypergeom}\left(a\,\left[\right]\,z\right)$

${\left(1-z\right)}^{-a}$

$\mathrm{hypergeom}\left(\left[\right]\,1\,-\frac{z^2}{4}\right)$

$\mathrm{BesselJ}\left(0\,z\right)$

$\mathrm{hypergeom}\left(\left[-10\,10\right]\,\frac{1}{2}\,\frac{1-z}{2}\right)$

$512z^{10}-1280z^8+1120z^6-400z^4+50z^2-1$