Difference between revisions of "Kelvin ber"

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File:Domcolkelvinbersub0.png|[[Domain coloring]] of $\mathrm{ber}_0$.
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File:Kelvinber,n=0plot.png|Graph of $\mathrm{ber}_0$.
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File:Kelvinber,n=0.5plot.png|Graph of $\mathrm{ber}_{\frac{1}{2}}$.
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File:Kelvinber,n=1plot.png|Graph of $\mathrm{ber}_1$.
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File:Kelvinber,n=2plot.png|Graph of $\mathrm{ber}_2$.
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File:Complexkelvinber,n=0plot.png|[[Domain coloring]] of $\mathrm{ber}_0$.
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File:Complexkelvinber,n=1plot.png|[[Domain coloring]] of $\mathrm{ber}_1$.
 
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=References=
 
=References=
[http://mathworld.wolfram.com/Ber.html] <br />
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* {{BookReference|Higher Transcendental Functions Volume II|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=findme|next=Kelvin bei}}: $\S 7.2.3 (19)$
  
<center>{{:Kelvin functions footer}}</center>
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[[Category:SpecialFunction]]
  
[[Category:SpecialFunction]]
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{{:Kelvin functions footer}}

Latest revision as of 05:41, 4 March 2018

The $\mathrm{ber}_{\nu}$ function is defined as $$\mathrm{ber}_{\nu}(z)=\mathrm{Re} \hspace{2pt} J_{\nu} \left( z e^{\frac{3\pi i}{4}} \right),$$ where $\mathrm{Re}$ denotes the real part of a complex number and $J_{\nu}$ denotes the Bessel function of the first kind.

References

Kelvin functions