Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a9qk)

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=3, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=3, b₁=7/2

http://functions.wolfram.com/07.25.03.a9qk.01

Input Form

HypergeometricPFQ[{-(3/2), 3}, {7/2, 6}, -z] == -((20 (36 - 78 z + 143 z^2))/(1001 z^5)) + (5 (6912 - 8064 z + 15936 z^2 - 5907 z^3 + 3798 z^4 + 2980 z^5 + 280 z^6))/ (E^z (48048 z^5)) + (5 Sqrt[Pi] (27027 - 10296 z + 10296 z^2 + 6240 z^3 + 560 z^4) Erf[Sqrt[z]])/(96096 z^(5/2))

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]