Kelvin function of the second kind: Representations through more general functions (formula 03.20.26.0004)

KelvinKer

$Mathematica Notation$

Bessel-Type Functions

KelvinKer[nu,z]

Representations through more general functions

Through hypergeometric functions

Involving hypergeometric U

http://functions.wolfram.com/03.20.26.0004.01

Input Form

KelvinKer[\[Nu], z] == 2^(-1 + \[Nu]) E^((-(-1)^(1/4)) z - (I Pi \[Nu])/4) Sqrt[Pi] z^\[Nu] HypergeometricU[1/2 + \[Nu], 1 + 2 \[Nu], 2 (-1)^(1/4) z] + ((-1)^(\[Nu]/4) 2^(-1 + \[Nu]) Sqrt[Pi] z^\[Nu] HypergeometricU[1/2 + \[Nu], 1 + 2 \[Nu], 2 (-1)^(3/4) z])/ E^((-1)^(3/4) z) + 2^(-3 - \[Nu]) E^((3 I Pi \[Nu])/4) z^\[Nu] ((-I) Pi - 4 Log[z] + 4 Log[(-1)^(1/4) z]) Hypergeometric0F1Regularized[ 1 + \[Nu], (I z^2)/4] + (-1)^((5 \[Nu])/4) 2^(-3 - \[Nu]) z^\[Nu] (I Pi - 4 Log[z] + 4 Log[(-1)^(3/4) z]) Hypergeometric0F1Regularized[ 1 + \[Nu], -((I z^2)/4)] /; Element[\[Nu], Integers]

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]