Kelvin function of the second kind: Representations through more general functions (formula 03.20.26.0051)

KelvinKer

$Mathematica Notation$

Bessel-Type Functions

KelvinKer[nu,z]

Representations through more general functions

Through Meijer G

Classical cases involving ₀F^~₁

http://functions.wolfram.com/03.20.26.0051.01

Input Form

Hypergeometric0F1Regularized[\[Nu] + 1, (I z^2)/4] KelvinKer[\[Nu], z] == ((1/8) Sqrt[Pi] ((I MeijerG[{{}, {(5 \[Nu])/4}}, {{(2 - \[Nu])/4, -(\[Nu]/4), \[Nu]/4}, {-((3 \[Nu])/4), (5 \[Nu])/4}}, z^4/64] + MeijerG[{{}, {(2 + 5 \[Nu])/4}}, {{(2 - \[Nu])/4, -(\[Nu]/4), \[Nu]/4}, {-((3 \[Nu])/4), (2 + 5 \[Nu])/4}}, z^4/64])/ 2^(\[Nu]/2) + (1/(Sqrt[2] Pi)) ((-I) MeijerG[{{(1 - \[Nu])/4, (3 - \[Nu])/4}, {}}, {{(2 - \[Nu])/4, \[Nu]/4, (2 + \[Nu])/4}, {(2 - 3 \[Nu])/4, -((3 \[Nu])/4), -(\[Nu]/4)}}, z^4/16] + MeijerG[{{(1 - \[Nu])/4, (3 - \[Nu])/4}, {}}, {{-(\[Nu]/4), \[Nu]/4, (2 + \[Nu])/4}, {(2 - 3 \[Nu])/4, (2 - \[Nu])/4, -((3 \[Nu])/4)}}, z^4/16])))/E^((3/4) I Pi \[Nu]) /; -(Pi/4) <= Arg[z] <= Pi/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

KelvinKer[z]