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

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=3, a₂>=3

For fixed z and a₁=3, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3, a₂=11/2, b₁=-1/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(1/2), -(1/2)}, -z] == (1/945) (945 - 62370 z + 2436840 z^2 - 8126160 z^3 + 8129520 z^4 - 3428832 z^5 + 698432 z^6 - 71424 z^7 + 3488 z^8 - 64 z^9) + ((16/945) Sqrt[Pi] (25200 z^(3/2) - 292320 z^(5/2) + 693000 z^(7/2) - 598080 z^(9/2) + 234150 z^(11/2) - 45780 z^(13/2) + 4571 z^(15/2) - 220 z^(17/2) + 4 z^(19/2)) 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]