Generalized hypergeometric function (mpmath, SymPy, WMA)
HypergeometricPFQ[${a_1, ..., a_p}, {b_1, ..., b_q}, z$]HypergeometricPFQ[{2}, {2}, 1]
Result is symbollicaly simplified by default:
HypergeometricPFQ[{3}, {2}, 1]
unless a numerical evaluation is explicitly requested:
HypergeometricPFQ[{3}, {2}, 1] // N
HypergeometricPFQ[{3}, {2}, 1.]
Plot[HypergeometricPFQ[{1, 1}, {3, 3, 3}, x], {x, -30, 30}]
HypergeometricPFQ[{1, 1, 2}, {3, 3}, z]
The following special cases are handled:
HypergeometricPFQ[{}, {}, z]
HypergeometricPFQ[{0}, {b}, z]
HypergeometricPFQ[{1, 1, 3}, {2, 2}, x]
HypergeometricPFQ evaluates to a polynomial if any of the parameters $a_k$ is a non-positive integer:
HypergeometricPFQ[{-2, a}, {b}, x]
Value at origin:
HypergeometricPFQ[{a1, b2, a3}, {b1, b2, b3}, 0]