Difference between revisions of "Kelvin bei"

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File:Kelvinbei,n=0plot.png|Graph of $\mathrm{bei}_0$.
 
File:Kelvinbei,n=0plot.png|Graph of $\mathrm{bei}_0$.
 
File:Kelvinbei,n=1plot.png|Graph of $\mathrm{bei}_1$.
 
File:Kelvinbei,n=1plot.png|Graph of $\mathrm{bei}_1$.
File:Domcolkelvinbeisub0.png|[[Domain coloring]] of $\mathrm{bei}_0$.
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File:Complexkelvinbei,n=0plot.png|[[Domain coloring]] of $\mathrm{bei}_0$.
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File:Complexkelvinbei,n=1plot.png|[[Domain coloring]] of $\mathrm{bei}_1$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
[[Category:SpecialFunction]]
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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 ber|next=Kelvin ker}}: $\S 7.2.3 (19)$
  
 
{{:Kelvin functions footer}}
 
{{:Kelvin functions footer}}
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[[Category:SpecialFunction]]

Latest revision as of 05:42, 4 March 2018

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

Properties

References

Kelvin functions