Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a90p)

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

For fixed z and a₁=-11/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a90p.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(1/2), 23/4}, -z] == -((19 (2 Sqrt[z] (278604451125 - 212270058000 z - 22313491200 z^2 - 4612608000 z^3 - 9727180800 z^4 + 10868490240 z^5 + 6962544640 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (835813353375 - 1910430522000 z + 3632428800 z^2 - 19372953600 z^3 - 7947878400 z^4 + 6967787520 z^5 + 6794772480 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-835813353375 + 127362034800 z - 3632428800 z^2 - 5748019200 z^3 - 10218700800 z^4 + 9232711680 z^5 + 6895435776 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (392586854400 Sqrt[2] z^(17/4)))

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]