Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9043)

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`=9/2

http://functions.wolfram.com/07.22.03.9043.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 17/4}, -z] == ((2 Sqrt[z] (83376713031987375 - 213243435859053600 z + 1077561818057894400 z^2 + 1047798662696755200 z^3 + 181539369123840000 z^4 + 9981090531901440 z^5 + 208241053138944 z^6 + 1679869083648 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 - 3 (138961188386645625 - 315544072563720000 z + 376122411855590400 z^2 + 902439502342963200 z^3 + 173102697647308800 z^4 + 9801331900416000 z^5 + 206777509478400 z^6 + 1676110987264 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (195801598134016875 - 362104043192892000 z + 444739333335897600 z^2 + 920880347821056000 z^3 + 174253577895936000 z^4 + 9826550415360000 z^5 + 206985379184640 z^6 + 1676647858176 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(815438053424332800 Sqrt[2] z^(11/4))

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]