Difference between revisions of "Kelvin kei"

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The $\mathrm{bei}_{\nu}$ function is defined as
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The $\mathrm{kei}_{\nu}$ function is defined as
$$\mathrm{ber}(z)=\mathrm{Im} \hspace{2pt} K_{\nu} \left( x e^{\frac{\pi i}{4}} \right),$$
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$$\mathrm{kei}_{\nu}(z)=\mathrm{Im} \left[ e^{-\frac{\nu \pi i}{2}} K_{\nu} \left( z e^{\frac{\pi i}{4}} \right) \right],$$
 
where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $K_{\nu}$ denotes the [[Modified Bessel K sub nu|modified Bessel $K_{\nu}$]].
 
where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $K_{\nu}$ denotes the [[Modified Bessel K sub nu|modified Bessel $K_{\nu}$]].
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Domcolkelvinkeisub0.png|[[Domain coloring]] of $\mathrm{kei}_0$.
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File:Complexkelvinkei,n=0plot.png|[[Domain coloring]] of $\mathrm{kei}_0$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
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=Properties=
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=References=
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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 ker|next=findme}}: $\S 7.2.3 (20)$
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{{:Kelvin functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 05:42, 4 March 2018

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

Properties

References

Kelvin functions