Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8315)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8315.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 9/4}, -z] == (Sqrt[Pi] (-7905853580625 + 885455601030000 z + 2833457923296000 z^2 + 1199347269120000 z^3 + 134192701440000 z^4 + 5051960524800 z^5 + 67528294400 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(7905853580625 + 129358925488800 z + 68131481644800 z^2 + 8106056663040 z^3 + 311852728320 z^4 + 4204789760 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (39043389802725 + 165795015304800 z + 73505947334400 z^2 + 8329529671680 z^3 + 314963066880 z^4 + 4217372672 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/ (1379636084736000 z^(5/4))

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]