Difference between revisions of "Kelvin bei"

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The $\mathrm{bei}_{\nu}$ function is defined as
 
The $\mathrm{bei}_{\nu}$ function is defined as
$$\mathrm{ber}(z)=\mathrm{Im} \hspace{2pt} J_{\nu} \left( x e^{\frac{3\pi i}{4}} \right),$$
+
$$\mathrm{bei}_{\nu}(z)=\mathrm{Im} \hspace{2pt} J_{\nu} \left( z e^{\frac{3\pi i}{4}} \right),$$
where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $J_{\nu}$ denotes the [[Bessel J sub nu|Bessel function of the first kind]].
+
where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Domcolkelvinbeisub0.png|[[Domain coloring]] 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:Complexkelvinbei,n=0plot.png|[[Domain coloring]] of $\mathrm{bei}_0$.
 +
File:Complexkelvinbei,n=1plot.png|[[Domain coloring]] of $\mathrm{bei}_1$.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
<center>{{:Kelvin functions footer}}</center>
+
=Properties=
 +
 
 +
=References=
 +
* {{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}}
 +
 
 +
[[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