Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8569)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.8569.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 23/4}, -z] == -((19 (Sqrt[Pi] (5485155330348559490625 + 1427032281066291900000 z + 252447971097722400000 z^2 + 46628196681830400000 z^3 + 15006775943577600000 z^4 - 11525203924667596800 z^5 + 1463517958687948800 z^6 - 87455788380979200 z^7 + 3104939232460800 z^8 - 72155450572800 z^9 + 1099511627776 z^10) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (1828385110116186496875 - 360155766173873670000 z + 1780938067708800000 z^2 + 1134486608726016000 z^3 - 740392638883430400 z^4 + 92587909762252800 z^5 - 5504396867665920 z^6 + 194932459438080 z^7 - 4522600562688 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + (-5485155330348559490625 + 4423800071305504890000 z - 216205881419848320000 z^2 + 2324767640832000000 z^3 - 835930126467072000 z^4 + 97495502133657600 z^5 - 5666831188623360 z^6 + 198540231966720 z^7 - 4574140170240 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/ (383031148307860684800 z^(19/4)))

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]