Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1038)

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=-11/2, a₂>=-11/2

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

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

http://functions.wolfram.com/07.25.03.1038.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {7/2, 5}, z] == (4 (6 + 114 z - 969 z^2 + 1615 z^3))/(4199 z^4) + (1/(451476480 z^4)) (E^z (-2580480 - 46448640 z + 246243375 z^2 - 291538170 z^3 + 140332500 z^4 - 33300696 z^5 + 4203472 z^6 - 284640 z^7 + 9664 z^8 - 128 z^9)) + (1/(902952960 z^(5/2))) (Sqrt[Pi] (218243025 - 698377680 z + 698377680 z^2 - 310390080 z^3 + 70543200 z^4 - 8682240 z^5 + 578816 z^6 - 19456 z^7 + 256 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]