Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8815)

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`=1/2

http://functions.wolfram.com/07.22.03.8815.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, -(19/4)}, -z] == (1/(4334247225 z^(1/4))) (Sqrt[2] ((4334247225 - 912473100 z - 12652960320 z^2 + 4222374912 z^3 - 589381632 z^4 + 49545216 z^5 - 4194304 z^6) BesselJ[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-1444749075 + 2230489800 z - 604840320 z^2 + 79865856 z^3 - 6651904 z^4 + 524288 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (4334247225 - 4162611600 z + 1181456640 z^2 - 157667328 z^3 + 13172736 z^4 - 1048576 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]