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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(5/2), 9/2}, z] == -((1/(720 z^3)) (7 (10800 - 3600 z + 1080 z^2 - 360 z^3 + 210 z^4 - 270 z^5 + 1035 z^6 + 826 z^7 + 156 z^8 + 8 z^9))) - (1/(1440 z^(7/2))) (7 E^z Sqrt[Pi] (-10800 + 10800 z - 5400 z^2 + 1800 z^3 - 450 z^4 + 90 z^5 - 15 z^6 + 2760 z^7 + 1800 z^8 + 320 z^9 + 16 z^10) 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]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]