Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9421)

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`=1/2

http://functions.wolfram.com/07.22.03.9421.01

Input Form

HypergeometricPFQ[{-(19/4)}, {1/2, 11/4}, -z] == ((2 Sqrt[z] (-3273645375 + 243171957600 z + 1405080518400 z^2 + 695918346240 z^3 + 74124820480 z^4 + 2204106752 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (-9820936125 - 41902660800 z + 1071615916800 z^2 + 653097369600 z^3 + 72775434240 z^4 + 2193620992 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (9820936125 + 62853991200 z + 1256311330560 z^2 + 678217236480 z^3 + 73580347392 z^4 + 2199912448 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (524255846400 Sqrt[2] z^(5/4))

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]