Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.7304)

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=3, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=3, b₁=5

http://functions.wolfram.com/07.25.03.7304.01

Input Form

HypergeometricPFQ[{-(7/2), 3}, {5, 11/2}, z] == (168 (-3 + 5 z))/(143 z^4) + (1/(23429120 z^4)) (E^z (58926735 - 42273210 z - 11176620 z^2 - 7260120 z^3 + 8703440 z^4 - 1960928 z^5 + 159168 z^6 - 4224 z^7)) + (1/(46858240 z^(9/2))) (Sqrt[Pi] (23648625 - 162162000 z + 75675600 z^2 + 20180160 z^3 + 21621600 z^4 - 19219200 z^5 + 4076800 z^6 - 322560 z^7 + 8448 z^8) Erfi[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]