Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9287)

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`=-5/2

http://functions.wolfram.com/07.22.03.9287.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(5/2), 21/4}, -z] == (221 (Sqrt[Pi] (7872835015670625 + 3229881032070000 z + 998610560640000 z^2 + 392436430848000 z^3 + 627898289356800 z^4 - 304435534233600 z^5 + 66271680921600 z^6 - 13770738892800 z^7 - 3672197038080 z^8 - 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-7872835015670625 + 5167809651312000 z + 313849033344000 z^2 + 36404121600000 z^3 - 20773689753600 z^4 + 4243335413760 z^5 - 661357854720 z^6 - 225485783040 z^7 - 4294967296 z^8) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-2624278338556875 + 123043086936000 z - 34583915520000 z^2 - 42277319884800 z^3 + 19707228979200 z^4 - 4220119941120 z^5 + 819399229440 z^6 + 228707008512 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/ (166246158119731200 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]