Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8173)

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/07.22.03.8173.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 11/4}, -z] == ((2 Sqrt[z] (-518198806125 + 4548713598000 z - 7934120812800 z^2 + 10215009792000 z^3 + 11427382886400 z^4 + 1312633651200 z^5 + 37664849920 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (-1554596418375 - 637783146000 z - 5435966764800 z^2 + 4881445171200 z^3 + 10667129241600 z^4 + 1289544007680 z^5 + 37497077760 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1554596418375 + 3954255505200 z - 7826697964800 z^2 + 7806581452800 z^3 + 11113443164160 z^4 + 1303322296320 z^5 + 37597741056 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(11101888512000 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]