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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(9/2), 5/2}, -z] == (1/(37800 z)) (75600 + 63000 z + 37800 z^2 + 23400 z^3 + 18270 z^4 + 22050 z^5 + 74445 z^6 - 47588 z^7 + 9000 z^8 - 656 z^9 + 16 z^10) + (1/(75600 z^(3/2))) ((Sqrt[Pi] (-75600 - 75600 z - 37800 z^2 - 12600 z^3 - 3150 z^4 - 630 z^5 - 105 z^6 - 188970 z^7 + 103560 z^8 - 18640 z^9 + 1328 z^10 - 32 z^11) 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]