Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8135)

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`=-5/2

http://functions.wolfram.com/07.22.03.8135.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 21/4}, -z] == (221 (Sqrt[Pi] (1629676848243819375 + 742872637376100000 z + 258390482565600000 z^2 + 116049058836480000 z^3 + 216624909828096000 z^4 - 126036311172710400 z^5 + 34295594876928000 z^6 - 9501809836032000 z^7 - 3800723934412800 z^8 - 142249316843520 z^9 - 1099511627776 z^10) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(1629676848243819375 - 995449334083974000 z - 92528401375872000 z^2 - 7719858026496000 z^3 + 8015561913139200 z^4 - 2080529606246400 z^5 + 401716008714240 z^6 + 229463996497920 z^7 + 8826157793280 z^8 + 68719476736 z^9)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-543225616081273125 + 707497749882000 z - 13064938685568000 z^2 - 14311042666905600 z^3 + 8151972279091200 z^4 - 2177830748160000 z^5 + 552795509882880 z^6 + 235906447441920 z^7 + 8877697400832 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/(59848616923103232000 z^(17/4))

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]