Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.adpy)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=4, b₁>=-11/2

For fixed z and a₁=1/2, a₂=4, b₁=-5/2

http://functions.wolfram.com/07.25.03.adpy.01

Input Form

HypergeometricPFQ[{1/2, 4}, {-(5/2), -(3/2)}, z] == (1/135) (135 + 72 z + 360 z^2 - 7200 z^3 - 27912 z^4 - 20232 z^5 - 5076 z^6 - 496 z^7 - 16 z^8) - (2/135) E^z Sqrt[Pi] (7722 z^(7/2) + 18018 z^(9/2) + 11271 z^(11/2) + 2658 z^(13/2) + 252 z^(15/2) + 8 z^(17/2)) Erf[Sqrt[z]]

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)

2007-05-02

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]