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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=5, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5, b₁=-3/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(3/2), 1/2}, -z] == (1/108) (108 + 1800 z + 25200 z^2 - 103572 z^3 + 93456 z^4 - 32175 z^5 + 4914 z^6 - 332 z^7 + 8 z^8) + ((1/216) Sqrt[Pi] (-108108 z^(5/2) + 277992 z^(7/2) - 214929 z^(9/2) + 68952 z^(11/2) - 10152 z^(13/2) + 672 z^(15/2) - 16 z^(17/2)) Erfi[Sqrt[z]])/E^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]