Kelvin function of the second kind: Integral transforms (formula 03.20.22.0001)

KelvinKer

$Mathematica Notation$

Bessel-Type Functions

KelvinKer[nu,z]

Integral transforms

Laplace transforms

http://functions.wolfram.com/03.20.22.0001.01

Input Form

LaplaceTransform[KelvinKer[\[Nu], t], t, z] == 2^(-3 - \[Nu]) Pi z^(-3 - \[Nu]) (4^(1 + \[Nu]) z^(2 + 2 \[Nu]) Cos[(3 Pi \[Nu])/4] Csc[Pi \[Nu]] HypergeometricPFQ[ {1/4 - \[Nu]/4, 1/2 - \[Nu]/4, 3/4 - \[Nu]/4, 1 - \[Nu]/4}, {1/2, 1/2 - \[Nu]/2, 1 - \[Nu]/2}, -(1/z^4)] - z^2 Csc[(Pi \[Nu])/4] Sec[(Pi \[Nu])/2] HypergeometricPFQ[ {1/4 + \[Nu]/4, 1/2 + \[Nu]/4, 3/4 + \[Nu]/4, 1 + \[Nu]/4}, {1/2, 1/2 + \[Nu]/2, 1 + \[Nu]/2}, -(1/z^4)] - Csc[Pi \[Nu]] ((2 + \[Nu]) Sin[(Pi \[Nu])/4] HypergeometricPFQ[ {3/4 + \[Nu]/4, 1 + \[Nu]/4, 5/4 + \[Nu]/4, 3/2 + \[Nu]/4}, {3/2, 1 + \[Nu]/2, 3/2 + \[Nu]/2}, -(1/z^4)] - z^(2 \[Nu]) (2^(1 + 2 \[Nu]) - 4^\[Nu] \[Nu]) Sin[(3 Pi \[Nu])/4] HypergeometricPFQ[{3/4 - \[Nu]/4, 1 - \[Nu]/4, 5/4 - \[Nu]/4, 3/2 - \[Nu]/4}, {3/2, 1 - \[Nu]/2, 3/2 - \[Nu]/2}, -(1/z^4)])) /; Abs[Re[\[Nu]]] < 1 && Re[z] > -(1/Sqrt[2])

Standard Form

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MathML Form

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

2007-05-02

KelvinKer[z]