Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afu1)

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`=9/2

http://functions.wolfram.com/07.22.03.afu1.01

Input Form

HypergeometricPFQ[{19/4}, {9/2, -(23/4)}, -z] == (1/(399750120 Sqrt[2] z^(9/4))) ((4 z (110924889075 - 30446040240 z + 4631477760 z^2 - 322560000 z^3 - 27328512 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (184874815125 - 67509842400 z + 11236538880 z^2 - 1157775360 z^3 - 19333120 z^4 + 6291456 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (2773122226875 - 1259147389500 z + 246136363200 z^2 - 29557463040 z^3 + 980582400 z^4 + 169082880 z^5 - 4194304 z^6) 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]