Kelvin function of the second kind: Representations through more general functions (formula 03.19.26.0002)

KelvinKei

$Mathematica Notation$

Bessel-Type Functions

KelvinKei[nu,z]

Representations through more general functions

Through hypergeometric functions

Involving _pF_q

http://functions.wolfram.com/03.19.26.0002.01

Input Form

KelvinKei[\[Nu], z] == (-2^(-3 + \[Nu])) z^(2 - \[Nu]) Cos[(3 Pi \[Nu])/4] Gamma[-1 + \[Nu]] HypergeometricPFQ[{}, {3/2, (3 - \[Nu])/2, 1 - \[Nu]/2}, -(z^4/256)] - 2^(-3 - \[Nu]) z^(2 + \[Nu]) Cos[(Pi \[Nu])/4] Gamma[-1 - \[Nu]] HypergeometricPFQ[{}, {3/2, (3 + \[Nu])/2, (2 + \[Nu])/2}, -(z^4/256)] - 2^(-1 - \[Nu]) z^\[Nu] Gamma[-\[Nu]] HypergeometricPFQ[{}, {1/2, (1 + \[Nu])/2, (2 + \[Nu])/2}, -(z^4/256)] Sin[(Pi \[Nu])/4] - (2^(-1 + \[Nu]) Gamma[\[Nu]] HypergeometricPFQ[{}, {1/2, (1 - \[Nu])/2, 1 - \[Nu]/2}, -(z^4/256)] Sin[(3 Pi \[Nu])/4])/ z^\[Nu] /; !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

KelvinKei[z]