Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8353)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8353.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(1/4)}, -z] == -(((16 z (-12758449725 + 126868291200 z + 189797447700 z^2 + 42305667840 z^3 + 2562508800 z^4 + 49217536 z^5 + 262144 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-10016466075 + 112556077200 z + 334257953400 z^2 + 81567440640 z^3 + 5064376320 z^4 + 98107392 z^5 + 524288 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-30049398225 - 228947796000 z + 1472937177600 z^2 + 2882180750400 z^3 + 666940538880 z^4 + 40804909056 z^5 + 786432000 z^6 + 4194304 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(190779907500 Sqrt[2] z^(3/4)))

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]