Kelvin function of the first kind: Representations through more general functions (formula 03.17.26.0002)

KelvinBei

$Mathematica Notation$

Bessel-Type Functions

KelvinBei[nu,z]

Representations through more general functions

Through hypergeometric functions

Involving _pF_q

http://functions.wolfram.com/03.17.26.0002.01

Input Form

KelvinBei[\[Nu], z] == (1/Gamma[\[Nu] + 1]) Sin[(3 Pi \[Nu])/4] (z/2)^\[Nu] HypergeometricPFQ[{}, {1/2, (\[Nu] + 1)/2, \[Nu]/2 + 1}, -(z^4/256)] + (1/Gamma[\[Nu] + 2]) Cos[(3 Pi \[Nu])/4] (z/2)^(\[Nu] + 2) HypergeometricPFQ[{}, {3/2, (\[Nu] + 3)/2, \[Nu]/2 + 1}, -(z^4/256)] /; !(Element[-\[Nu], Integers] && -\[Nu] > 0)

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

KelvinBei[z]