Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9591)

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`=9/2

http://functions.wolfram.com/07.22.03.9591.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(11/4)}, -z] == (1/(1407047241600 z^(7/2))) (-2 Sqrt[z] (5155991465625 - 714964149900 z + 125707982400 z^2 - 12869176320 z^3 + 1873428480 z^4 - 554434560 z^5 + 641728512 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] - 16777216 Sqrt[Pi] z^(29/4) (627 + 16 z) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (5155991465625 - 7589619437400 z - 754247894400 z^2 + 78875596800 z^3 - 9196830720 z^4 + 1816657920 z^5 - 931135488 z^6 + 5234491392 z^7 + 134217728 z^8) 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]