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

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`=-11/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), 21/4}, -z] == (221 (6 Sqrt[z] (-67469484557475 - 58908267910800 z + 19358953447680 z^2 - 2390054768640 z^3 + 173057310720 z^4 - 9689890816 z^5 + 285212672 z^6) BesselJ[1/4, Sqrt[z]]^2 + (1012042268362125 + 1603298520608400 z - 744616728979200 z^2 + 117723648430080 z^3 - 10077847879680 z^4 + 609878016000 z^5 - 26021462016 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 6 Sqrt[z] (337347422787375 - 185241661743600 z + 37311949382400 z^2 - 3861705093120 z^3 + 259735879680 z^4 - 13185843200 z^5 + 318767104 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(839295959040 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]