Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8pz)

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`=7/2

http://functions.wolfram.com/07.22.03.a8pz.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, 21/4}, -z] == (17 (2 Sqrt[z] (310919283675 + 1233047415600 z - 4762114156800 z^2 + 15660152893440 z^3 + 12075599462400 z^4 + 1331407355904 z^5 + 37799067648 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (518198806125 + 2423575954800 z - 7029787564800 z^2 + 6831536025600 z^3 + 10964671856640 z^4 + 1298729533440 z^5 + 37564186624 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, 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[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(183386167050240 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]