Generalized hypergeometric function 2F2: Transformations (formula 07.25.16.0002)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Transformations

Products, sums, and powers of the direct function

Products of the direct function

http://functions.wolfram.com/07.25.16.0002.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, c z] HypergeometricPFQ[{Subscript[\[Alpha], 1], Subscript[\[Alpha], 2]}, {Subscript[\[Beta], 1], Subscript[\[Beta], 2]}, d z] == Sum[((Pochhammer[Subscript[a, 1], m] Pochhammer[Subscript[a, 2], m] c^m)/ (Pochhammer[Subscript[b, 1], m] Pochhammer[Subscript[b, 2], m] m!)) ((Pochhammer[Subscript[\[Alpha], 1], k - m] Pochhammer[Subscript[\[Alpha], 2], k - m] d^(k - m))/ (Pochhammer[Subscript[\[Beta], 1], k - m] Pochhammer[Subscript[\[Beta], 2], k - m] (k - m)!)) z^k, {k, 0, Infinity}, {m, 0, k}]

Standard Form

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MathML Form

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