Difference between revisions of "Kelvin ker"

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File:Domcolkelvinkersub0.png|[[Domain coloring]] of $\mathrm{ker}_0$.
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File:Kelvinker,n=0plot.png|Graph of $\mathrm{ker}_0$.
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File:Complexkelvinker,n=0plot.png|[[Domain coloring]] of $\mathrm{ker}_0$.
 
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=Properties=
  
 
=References=
 
=References=
[http://mathworld.wolfram.com/Ker.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=Kelvin bei|next=Kelvin kei}}: $\S 7.2.3 (20)$
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{{:Kelvin functions footer}}
  
<center>{{:Kelvin functions footer}}</center>
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[[Category:SpecialFunction]]

Latest revision as of 05:42, 4 March 2018

The $\mathrm{ker}_{\nu}$ function is defined as $$\mathrm{ker}_{\nu}(z)=\mathrm{Re} \left[ e^{-\frac{\nu \pi i}{2}} K_{\nu} \left( z e^{\frac{\pi i}{4}} \right) \right],$$ where $\mathrm{Re}$ denotes the real part of a complex number and $K_{\nu}$ denotes the modified Bessel function $K_{\nu}$.

Properties

References

Kelvin functions