Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ch)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8ch.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 15/4}, -z] == ((2 z (-524431908000 + 4272715321875 z - 4377206433600 z^2 + 10896470956800 z^3 + 3063059251200 z^4 + 185502597120 z^5 + 3376414720 z^6 + 16777216 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (-3146591448000 + 8922366077625 z - 7731040917600 z^2 + 9256985337600 z^3 + 2952596275200 z^4 + 183420518400 z^5 + 3365928960 z^6 + 16777216 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (-1179971793000 - 2921834916000 z + 6480948248775 z^2 - 6188880297600 z^3 + 10197265478400 z^4 + 3017971630080 z^5 + 184665047040 z^6 + 3372220416 z^7 + 16777216 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(12669516288000 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]