Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8512)

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=6, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=6, b₁=5

http://functions.wolfram.com/07.25.03.8512.01

Input Form

HypergeometricPFQ[{-(7/2), 6}, {5, 11/2}, -z] == (1/(5242880 z^4)) ((3 (-11025 + 68250 z - 128940 z^2 + 231000 z^3 + 867280 z^4 + 382432 z^5 + 52672 z^6 + 2176 z^7))/E^z) + (1/(10485760 z^(9/2))) (3 Sqrt[Pi] (11025 - 75600 z + 176400 z^2 - 329280 z^3 + 1058400 z^4 + 2069760 z^5 + 815360 z^6 + 107520 z^7 + 4352 z^8) Erf[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]