H-function

The Fox H-function is a very general function defined by H(z) = H_(p, q)^(m, n)[z|(a_1, α_1), ..., (a_p, α_p) (b_1, β_1), ..., (b_p, β_p)] = 1/(2π i) integral_C ( product_(j = 1)^m Γ(b_j - β_i s) product_(j = 1)^n Γ(1 - a_j + α_j s))/( product_(j = n + 1)^p Γ(a_j + α_j s) product_(j = m + 1)^q Γ(1 - b_j + β_j s)) z^s d s, where 0<=m<=q, 0<=n<=p, α_j, β_j>0, and a_j, b_j are complex numbers such that no pole of Γ(b_j - β_j s) for j = 1, 2, ..., m coincides with any pole of Γ(1 - a_j + α_j s) for j = 1, 2, ..., n . In addition C, is a contour in the complex s-plane from ω - i∞ to ω + i∞ such that (b_j + k)/β_j and (a_j - 1 - k)/α_j lie to the right and left of C, respectively.

Kampé de Fériet function | MacRobert's E-function | Meijer G-function