Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae21)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=5, b₁>=-11/2

For fixed z and a₁=1/2, a₂=5, b₁=-3/2

http://functions.wolfram.com/07.25.03.ae21.01

Input Form

HypergeometricPFQ[{1/2, 5}, {-(3/2), -(3/2)}, z] == (1/108) (108 + 120 z + 2160 z^2 + 32382 z^3 + 46976 z^4 + 21231 z^5 + 3890 z^6 + 300 z^7 + 8 z^8) + (1/216) E^z Sqrt[Pi] (18018 z^(5/2) + 97812 z^(7/2) + 111969 z^(9/2) + 46072 z^(11/2) + 8072 z^(13/2) + 608 z^(15/2) + 16 z^(17/2)) 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]