Kelvin function of the first kind: Representations through more general functions (formula 03.17.26.0078)

KelvinBei

$Mathematica Notation$

Bessel-Type Functions

KelvinBei[nu,z]

Representations through more general functions

Through Meijer G

Generalized cases involving Bessel J

http://functions.wolfram.com/03.17.26.0078.01

Input Form

BesselJ[\[Nu], z/(-1)^4^(-1)] KelvinBei[\[Nu], z] == ((-I) 2^(-1 - (3 \[Nu])/2) Sqrt[Pi] z^\[Nu] (z/(-1)^4^(-1))^\[Nu] (E^((3 I Pi \[Nu])/2) 2^((3 \[Nu])/2) Csc[Pi (3/4 + \[Nu])] MeijerG[{{(1 - \[Nu])/2}, {(1 - 2 \[Nu])/4}}, {{\[Nu]/2}, {-(\[Nu]/2), -((3 \[Nu])/2), (1 - 2 \[Nu])/4}}, (-1)^(1/4) z, 1/2] - MeijerG[{{}, {}}, {{\[Nu]/4}, {-(\[Nu]/4), (2 - \[Nu])/4, -((3 \[Nu])/4)}}, ((-1)^(1/4) z)/(2 Sqrt[2]), 1/4]))/(E^((3/4) I Pi \[Nu]) ((-1)^(1/4) z)^\[Nu])

Standard Form

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MathML Form

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</ci> </apply> </apply> </list> </list> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

KelvinBei[z]