Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8559)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.8559.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 13/4}, -z] == ((-2 Sqrt[z] (264687977879325 - 50790208669200 z - 333352182240000 z^2 + 80159959756800 z^3 - 7676928000000 z^4 + 401844731904 z^5 - 13035896832 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 + 3 (441146629798875 + 1047367482361200 z - 418786348780800 z^2 + 87575330304000 z^3 - 8049549312000 z^4 + 413647503360 z^5 - 13270777856 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 2 Sqrt[z] (1323439889396625 + 318764016370800 z - 402659402745600 z^2 + 86358995251200 z^3 - 7991952998400 z^4 + 411885895680 z^5 - 13237223424 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(490988136038400 Sqrt[2] z^(7/4))

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]