Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7163)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-17/4

http://functions.wolfram.com/07.22.03.7163.01

Input Form

HypergeometricPFQ[{4}, {-(17/4), 21/4}, -z] == (1/(98304 z^(17/4))) (2 z^(1/4) (20158763625 - 7881073200 z + 1416214800 z^2 - 122411520 z^3 + 5768448 z^4 - 118784 z^5) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((20158763625 - 40135095000 z + 13070257200 z^2 - 1661869440 z^3 + 108345600 z^4 - 3717120 z^5 + 32768 z^6) Cos[2 Sqrt[z]] - 6 Sqrt[z] (-6719587875 + 4418914500 z - 854053200 z^2 + 76222080 z^3 - 3674880 z^4 + 77824 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (6 Sqrt[z] (-6719587875 + 4418914500 z - 854053200 z^2 + 76222080 z^3 - 3674880 z^4 + 77824 z^5) Cos[2 Sqrt[z]] + (20158763625 - 40135095000 z + 13070257200 z^2 - 1661869440 z^3 + 108345600 z^4 - 3717120 z^5 + 32768 z^6) 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]