Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9333)

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`=-3/2

http://functions.wolfram.com/07.22.03.9333.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(3/2), 19/4}, -z] == ((2 Sqrt[z] (-47641361142375 + 26398676304000 z + 6033983155200 z^2 + 20295666892800 z^3 - 17872640409600 z^4 + 11214771978240 z^5 + 6918588334080 z^6 + 390842023936 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-142924083427125 + 296985108420000 z + 51288856819200 z^2 + 16090621747200 z^3 - 17137159372800 z^4 + 7497182085120 z^5 + 6681526272000 z^6 + 388157669376 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (142924083427125 + 7919602891200 z + 12067966310400 z^2 + 22279322419200 z^3 - 18613164441600 z^4 + 9629891297280 z^5 + 6822555549696 z^6 + 389768282112 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(45049341542400 Sqrt[2] z^(13/4))

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]