Kelvin function of the first kind: Representations through more general functions (formula 03.17.26.0086)

KelvinBei

$Mathematica Notation$

Bessel-Type Functions

KelvinBei[nu,z]

Representations through more general functions

Through Meijer G

Generalized cases involving ₀F₁

http://functions.wolfram.com/03.17.26.0086.01

Input Form

Hypergeometric0F1[1 + \[Nu], (I z^2)/4] KelvinBei[\[Nu], z] == ((-I) 2^(-1 - \[Nu]/2) Sqrt[Pi] z^\[Nu] Gamma[1 + \[Nu]] (E^((3 I Pi \[Nu])/2) 2^(3 (\[Nu]/2)) Csc[Pi (3/4 + \[Nu])] MeijerG[{{(1 - \[Nu])/2}, {(1 - 2 \[Nu])/4}}, {{\[Nu]/2}, {-(\[Nu]/2), -((3 \[Nu])/2), (1 - 2 \[Nu])/4}}, (-1)^(1/4) z, 1/2] - MeijerG[{{}, {}}, {{\[Nu]/4}, {-(\[Nu]/4), (2 - \[Nu])/4, -((3 \[Nu])/4)}}, ((-1)^(1/4) z)/(2 Sqrt[2]), 1/4]))/(E^((3/4) I Pi \[Nu]) ((-1)^(1/4) z)^\[Nu])

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]