Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9415)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.9415.01

Input Form

HypergeometricPFQ[{-(19/4)}, {1/2, 5/4}, -z] == (1/(2444083200 z^(1/4))) (Sqrt[Pi] (654729075 + 17459442000 z + 15962918400 z^2 + 2579865600 z^3 + 105840640 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(567312525 + 868775040 z + 155281920 z^2 + 6553600 z^3 + 65536 z^4)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (955523025 + 969996480 z + 160028160 z^2 + 6602752 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]