Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad9z)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ad9z.01

Input Form

HypergeometricPFQ[{9/4}, {-(11/2), 23/4}, -z] == (19 (2 Sqrt[z] (-583649791349625 + 629067370932000 z - 103268739974400 z^2 + 6174297292800 z^3 - 143796469760 z^4 + 973078528 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + (1750949374048875 - 4555315444680000 z + 1300538029190400 z^2 - 120398797209600 z^3 + 4421910528000 z^4 - 58703478784 z^5 + 134217728 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1750949374048875 - 819956780042400 z + 120494409235200 z^2 - 6767979724800 z^3 + 151388160000 z^4 - 989855744 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(2013265920 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]