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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=6, b₁>=-11/2

For fixed z and a₁=1/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{1/2, 6}, {-(9/2), 5/2}, -z] == (1/(75600 z)) (-75600 - 63000 z - 25200 z^2 - 4500 z^3 + 2070 z^4 + 4305 z^5 + 13440 z^6 - 4912 z^7 + 512 z^8 - 16 z^9) + (1/(151200 z^(3/2))) ((Sqrt[Pi] (75600 + 189000 z + 151200 z^2 + 69300 z^3 + 22050 z^4 + 5355 z^5 + 1050 z^6 - 31320 z^7 + 10320 z^8 - 1040 z^9 + 32 z^10) 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]