Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8an)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8an.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, -(3/4)}, -z] == (1/(553737600 z^(7/2))) (-2 Sqrt[z] (516891375 + 8108100 z + 59875200 z^2 - 35435520 z^3 + 55050240 z^4 + 7004160 z^5 + 131072 z^6) Cos[2 Sqrt[z]] - 8192 Sqrt[Pi] z^(21/4) (119625 + 13920 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (516891375 - 681080400 z - 134719200 z^2 + 88704000 z^3 - 71147520 z^4 + 479723520 z^5 + 56819712 z^6 + 1048576 z^7) 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]