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

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=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(7/2), -(1/2)}, -z] == (1/945) (945 - 6750 z - 56700 z^2 - 264600 z^3 - 2328480 z^4 + 6815952 z^5 - 5292300 z^6 + 1761540 z^7 - 290598 z^8 + 24628 z^9 - 1016 z^10 + 16 z^11) + ((1/945) Sqrt[Pi] (4375800 z^(9/2) - 8851050 z^(11/2) + 6054210 z^(13/2) - 1895721 z^(15/2) + 302424 z^(17/2) - 25128 z^(19/2) + 1024 z^(21/2) - 16 z^(23/2)) 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]