Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9705)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9705.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 7/4}, -z] == (1/(43599790080 z^(3/4))) (Sqrt[Pi] (-10384817625 + 33231416400 z - 10127669760 z^2 + 1059102720 z^3 - 50135040 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (1988367885 - 646842240 z + 66808320 z^2 - 3145728 z^3 + 65536 z^4) Cos[2 Sqrt[z]] + (10384817625 - 708765120 z + 69373440 z^2 - 3194880 z^3 + 65536 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]