Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acf9)

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=5/4, b_1`>=-11/2

For fixed z and a₁=5/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.acf9.01

Input Form

HypergeometricPFQ[{5/4}, {-(9/2), 21/4}, -z] == -((1/(11274289152 z^(17/4))) (221 (504735 Sqrt[Pi] (17137575 + 1807920 z + 103680 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((8649933917625 - 8314075677600 z + 1422238245120 z^2 - 68734156800 z^3 + 788529152 z^4) Cos[2 Sqrt[z]] + 4 Sqrt[z] (2883311305875 - 1013911668000 z + 91416764160 z^2 - 2291138560 z^3 + 8388608 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]