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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-7/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(7/2), -(5/2)}, z] == (1/70875) (70875 + 141750 z + 510300 z^2 + 8731800 z^3 - 454053600 z^4 - 5232427200 z^5 - 11539382400 z^6 - 9927423360 z^7 - 4222604160 z^8 - 992510880 z^9 - 135962400 z^10 - 11014320 z^11 - 514976 z^12 - 12736 z^13 - 128 z^14) - (1/70875) (8 E^z Sqrt[Pi] (183783600 z^(9/2) + 1085994000 z^(11/2) + 1898883000 z^(13/2) + 1458916200 z^(15/2) + 582816150 z^(17/2) + 131946570 z^(19/2) + 17653425 z^(21/2) + 1408200 z^(23/2) + 65160 z^(25/2) + 1600 z^(27/2) + 16 z^(29/2)) 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]