Generalized hypergeometric function: Specific values (formula 07.31.03.0006)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]

Specific values

Specialized values

Case _pF_qwith fixed a₁, ..., a_p

http://functions.wolfram.com/07.31.03.0006.01

Input Form

HypergeometricPFQ[{1, Subscript[a, 2], \[Ellipsis], Subscript[a, p]}, {3, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] == (2/z^2) (Product[(Subscript[b, j] - 2) (Subscript[b, j] - 1), {j, 2, q}]/ Product[(Subscript[a, j] - 2) (Subscript[a, j] - 1), {j, 2, p}]) (HypergeometricPFQ[{Subscript[a, 2] - 2, \[Ellipsis], Subscript[a, p] - 2}, {Subscript[b, 2] - 2, \[Ellipsis], Subscript[b, q] - 2}, z] - z (Product[Subscript[a, j] - 2, {j, 2, p}]/Product[Subscript[b, j] - 2, {j, 2, q}]) - 1)

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,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]