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

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, a₂>=1

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

For fixed z and a₁=1, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{1, 11/2}, {-(7/2), -(7/2)}, -z] == (1/10418625) (10418625 - 4677750 z + 4864860 z^2 - 16216200 z^3 + 551350800 z^4 - 15005904480 z^5 + 40300424640 z^6 - 35626421376 z^7 + 14270480640 z^8 - 2962675200 z^9 + 336681984 z^10 - 20908032 z^11 + 659456 z^12 - 8192 z^13) + (1/10418625) ((8192 Sqrt[Pi] (-362880 z^(9/2) + 3265920 z^(11/2) - 6531840 z^(13/2) + 5080320 z^(15/2) - 1905120 z^(17/2) + 381024 z^(19/2) - 42336 z^(21/2) + 2592 z^(23/2) - 81 z^(25/2) + z^(27/2)) 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]