Generalized hypergeometric function 2F2: Identities (formula 07.25.17.0020)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Identities

Functional identities

Division on even and odd parts and generalization

http://functions.wolfram.com/07.25.17.0020.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, z] == SuperPlus[A][z] + SuperMinus[A][z] /; SuperPlus[A][z] == HypergeometricPFQ[{Subscript[a, 1]/2, Subscript[a, 2]/2, (Subscript[a, 1] + 1)/2, (Subscript[a, 2] + 1)/2}, {1/2, Subscript[b, 1]/2, Subscript[b, 2]/2, (Subscript[b, 1] + 1)/2, (Subscript[b, 2] + 1)/2}, z^2/4] && SuperMinus[A][z] == ((z Subscript[a, 1] Subscript[a, 2])/(Subscript[b, 1] Subscript[b, 2])) HypergeometricPFQ[{(Subscript[a, 1] + 1)/2, (Subscript[a, 2] + 1)/2, (Subscript[a, 1] + 2)/2, (Subscript[a, 2] + 2)/2}, {3/2, (Subscript[b, 1] + 1)/2, (Subscript[b, 2] + 1)/2, (Subscript[b, 1] + 2)/2, (Subscript[b, 2] + 2)/2}, z^2/4]

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]