Generalized hypergeometric function 6F5: Primary definition (formula 07.30.02.0002)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]

Primary definition

http://functions.wolfram.com/07.30.02.0002.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, i], \[Ellipsis], Subscript[a, 6]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, j], \[Ellipsis], Subscript[b, 5]}, z] == Sum[(Pochhammer[Subscript[a, 1], k] Pochhammer[Subscript[a, 2], k] Pochhammer[Subscript[a, 3], k] Pochhammer[Subscript[a, 4], k] Pochhammer[Subscript[a, 5], k] Pochhammer[Subscript[a, 6], k] z^k)/ (Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k] Pochhammer[Subscript[b, 3], k] Pochhammer[Subscript[b, 4], k] Pochhammer[Subscript[b, 5], k] k!), {k, 0, n}] /; Subscript[a, i] == -n && Subscript[b, j] == -m && Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0 && m >= n

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]