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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(11/2), 9/2}, z] == (1/(35640 z^3)) (16329600 - 7257600 z + 2237760 z^2 - 534600 z^3 + 97200 z^4 - 10080 z^5 - 2520 z^6 + 3312 z^7 - 3747 z^8 + 10980 z^9 + 4488 z^10 + 496 z^11 + 16 z^12) + (1/(71280 z^(7/2))) (E^z Sqrt[Pi] (-16329600 + 18144000 z - 9979200 z^2 + 3628800 z^3 - 982800 z^4 + 211680 z^5 - 37800 z^6 + 5760 z^7 - 765 z^8 + 90 z^9 + 25992 z^10 + 9456 z^11 + 1008 z^12 + 32 z^13) 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]
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