Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8007)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8007.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), -(11/4)}, -z] == (1/218295) ((218295 - 335160 z - 18000 z^2 - 4224 z^3 + 1984 z^4 + 1024 z^5) Cos[2 Sqrt[z]] + 32 Sqrt[Pi] z^(15/4) (-1311 + 736 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 Sqrt[z] (218295 - 44100 z + 816 z^2 + 10752 z^3 - 5504 z^4 - 2048 z^5) Sin[2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]