Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9lz)

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`=7/2

http://functions.wolfram.com/07.22.03.a9lz.01

Input Form

HypergeometricPFQ[{-(9/4)}, {7/2, 21/4}, -z] == (17 (2 Sqrt[z] (1039863825 + 3697293600 z - 11376288000 z^2 + 24980668416 z^3 + 15783100416 z^4 + 1176502272 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 (1733106375 + 7394587200 z - 16432416000 z^2 + 12797706240 z^3 + 14778433536 z^4 + 1161822208 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (5199319125 + 11091880800 z - 17717356800 z^2 + 14250885120 z^3 + 14917238784 z^4 + 1163919360 z^5 + 16777216 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(265777053696 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]