Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7439)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-17/4

http://functions.wolfram.com/07.22.03.7439.01

Input Form

HypergeometricPFQ[{5}, {-(17/4), -(7/4)}, -z] == (1/626535) (3 (208845 - 140400 z + 172800 z^2 - 699080 z^3 - 466912 z^4 + 17920 z^5) - 4 Sqrt[Pi] z^(11/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-530955 + 330372 z - 238464 z^2 + 1024 z^3) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-530955 - 377568 z + 13568 z^2) Sin[2 Sqrt[z]]) - 4 Sqrt[Pi] z^(11/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-2 Sqrt[z] (-530955 - 377568 z + 13568 z^2) Cos[2 Sqrt[z]] + (-530955 + 330372 z - 238464 z^2 + 1024 z^3) 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]