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

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, a₂>=1

For fixed z and a₁=1, a₂=9/2, b₁>=-11/2

For fixed z and a₁=1, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1, 9/2}, {-(11/2), 6}, z] == (65 (-162792 - 7752 z + 204 z^2 - 12 z^3 + z^4))/(7 z^5) + (1/(72765 z^5)) (8 E^z (13749310575 - 13094581500 z + 6202696500 z^2 - 1945944000 z^3 + 454053600 z^4 - 83825280 z^5 + 12700800 z^6 - 1612800 z^7 + 172800 z^8 - 15360 z^9 + 1024 z^10))

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]