Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8979)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8979.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 1/4}, -z] == ((16 z (19694951955 + 159138483840 z + 174261151764 z^2 + 39089836800 z^3 + 2441005056 z^4 + 48168960 z^5 + 262144 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-1776226725 + 102934586160 z + 286730138520 z^2 + 74046728448 z^3 + 4798488576 z^4 + 95879168 z^5 + 524288 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-26643400875 - 50523782400 z + 969965176320 z^2 + 2355323987520 z^3 + 596891344896 z^4 + 38482182144 z^5 + 767557632 z^6 + 4194304 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(159691087710 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]