Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9199)

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=1, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=1, b₁=5/2

http://functions.wolfram.com/07.25.03.9199.01

Input Form

HypergeometricPFQ[{-(5/2), 1}, {5/2, 6}, -z] == -((5 (-24 + 72 z - 156 z^2 + 572 z^3 + 1287 z^4))/(3003 z^5)) + (-360 + 720 z - 1440 z^2 + 6720 z^3 + 7575 z^4 + 2226 z^5 + 236 z^6 + 8 z^7)/(E^z (9009 z^5)) + (Sqrt[Pi] (19305 + 17160 z + 4680 z^2 + 480 z^3 + 16 z^4) Erf[Sqrt[z]])/ (18018 z^(3/2))

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]