Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7tj)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a7tj.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, 5/4}, -z] == (1/(5151325410 Sqrt[2] z^(5/4))) ((4 z (2581301520 + 5865392169 z + 2642955840 z^2 + 282207744 z^3 + 8503296 z^4 + 65536 z^5) BesselJ[1/4, Sqrt[z]]^2 - 6 Sqrt[z] (18796050 + 3918498255 z + 2408150304 z^2 + 274864128 z^3 + 8445952 z^4 + 65536 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (140970375 + 451105200 z + 16547679540 z^2 + 9757891584 z^3 + 1103579136 z^4 + 33816576 z^5 + 262144 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]