Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8169)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8169.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 7/4}, -z] == ((2 Sqrt[z] (67664121525 - 170498671200 z + 309049378560 z^2 + 430110720000 z^3 + 60210479104 z^4 + 2040528896 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (-39861446625 - 80691811200 z + 120245748480 z^2 + 395711447040 z^3 + 58963329024 z^4 + 2030043136 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (39861446625 - 158075517600 z + 221597925120 z^2 + 415824297984 z^3 + 59706900480 z^4 + 2036334592 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (161902540800 Sqrt[2] z^(1/4))

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]