Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9063)

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/07.22.03.9063.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(11/4)}, -z] == -(((4 z (398434297818375 + 64552026357000 z - 3128776035840 z^2 - 26261799782400 z^3 + 8024900567040 z^4 - 1370519764992 z^5 + 410102267904 z^6 + 41573941248 z^7 + 536870912 z^8) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (664057163030625 + 48559407214500 z + 17034935299200 z^2 - 17891715179520 z^3 + 4797917429760 z^4 - 835745218560 z^5 + 187258896384 z^6 + 20552089600 z^7 + 268435456 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (9960857445459375 - 157018442490000 z + 160507741212000 z^2 + 111084956236800 z^3 - 136287671869440 z^4 + 37376415498240 z^5 - 6555162378240 z^6 + 1517801177088 z^7 + 164685152256 z^8 + 2147483648 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(40597023186720 Sqrt[2] z^(13/4)))

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]