Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6537)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-21/4

http://functions.wolfram.com/07.22.03.6537.01

Input Form

HypergeometricPFQ[{2}, {-(21/4), 13/4}, -z] == (1/(37128 z^(9/4))) (2 z^(1/4) (10135125 - 3783780 z + 598836 z^2 - 30976 z^3 + 256 z^4) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (10135125 - 6486480 z + 1108800 z^2 - 59904 z^3 + 512 z^4) Cos[2 Sqrt[z]] + (-10135125 + 19999980 z - 6153840 z^2 + 604800 z^3 - 15616 z^4) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((10135125 - 19999980 z + 6153840 z^2 - 604800 z^3 + 15616 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (10135125 - 6486480 z + 1108800 z^2 - 59904 z^3 + 512 z^4) 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]