Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a95x)

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`=7/2

http://functions.wolfram.com/07.22.03.a95x.01

Input Form

HypergeometricPFQ[{-(11/4)}, {7/2, 19/4}, -z] == ((2 Sqrt[z] (3714726015 + 30875644800 z - 44606225664 z^2 + 122475085824 z^3 + 32444841984 z^4 + 1577058304 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (11144178045 + 75645329760 z - 82383485184 z^2 + 104650850304 z^3 + 31487361024 z^4 + 1566572544 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-11144178045 + 54014216256 z - 65141556480 z^2 + 114949029888 z^3 + 32057131008 z^4 + 1572864000 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(142343405568 Sqrt[2] z^(13/4))

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]