Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8pd)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a8pd.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, -(1/4)}, -z] == (1/(3230304 z^(5/2))) (-2 Sqrt[z] (405405 + 294840 z - 403968 z^2 + 3164160 z^3 + 609280 z^4 + 16384 z^5) Cos[2 Sqrt[z]] - 256 Sqrt[Pi] z^(15/4) (51129 + 9568 z + 256 z^2) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - (-405405 + 245700 z - 673920 z^2 + 1379328 z^3 + 298496 z^4 + 8192 z^5) 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]