Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9237)

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`=-7/2

http://functions.wolfram.com/07.22.03.9237.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 19/4}, -z] == ((2 Sqrt[z] (-767555262849375 + 549972423000000 z + 70396470144000 z^2 + 73869155942400 z^3 - 30713226854400 z^4 + 4691601653760 z^5 - 451307110400 z^6 + 44023414784 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-2302665788548125 + 5158741327740000 z + 175991175360000 z^2 + 98331577344000 z^3 - 34245240422400 z^4 + 4997649530880 z^5 - 471607541760 z^6 + 41339060224 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (2302665788548125 - 246387645504000 z + 46930980096000 z^2 + 83616222412800 z^3 - 32063392972800 z^4 + 4813718814720 z^5 - 460635242496 z^6 + 42949672960 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(140153507020800 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]