Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8lz)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a8lz.01

Input Form

HypergeometricPFQ[{-(13/4)}, {1/2, 21/4}, -z] == (17 (2 Sqrt[z] (-54784404675 - 82410728400 z - 32691859200 z^2 + 174441738240 z^3 + 541136977920 z^4 + 241978834944 z^5 + 18169724928 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (-91307341125 - 202280878800 z - 54486432000 z^2 - 41513472000 z^3 + 354475376640 z^4 + 226476687360 z^5 + 17934843904 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-273922023375 - 22475653200 z - 26464838400 z^2 - 41513472000 z^3 + 376729436160 z^4 + 228615782400 z^5 + 17968398336 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (3357183836160 Sqrt[2] z^(15/4))

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]