Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8dz)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a8dz.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(11/2), 21/4}, -z] == -((17 (2 Sqrt[z] (2631309897741525 + 2961737373394800 z - 63268088083200 z^2 + 8503704760320 z^3 - 7509960622080 z^4 + 646834028544 z^5 - 21088960512 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (4385516496235875 + 8054818464092400 z - 1286451124358400 z^2 + 25397942169600 z^3 - 8108838420480 z^4 + 665683230720 z^5 - 21323841536 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (13156549488707625 - 3902850183632400 z + 189804264249600 z^2 + 14842953216000 z^3 - 8016654827520 z^4 + 662914990080 z^5 - 21290287104 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(214859765514240 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]