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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=-9/2

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

Input Form

HypergeometricPFQ[{1/4}, {-(9/2), 21/4}, -z] == (1/(180388626432 z^(17/4))) (221 (21945 Sqrt[Pi] (394164225 + 55442880 z + 4769280 z^2 + 376832 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((8649933917625 - 8009902177200 z + 1150117436160 z^2 - 35951185920 z^3 + 134217728 z^4) Cos[2 Sqrt[z]] - 8740 Sqrt[z] (-1319593275 + 417629520 z - 28608768 z^2 + 323584 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]