Difference between revisions of "Kelvin ber"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "The $\mathrm{ber}_{\nu}$ function is defined as $$\mathrm{ber}(z)=\mathrm{Re} J_{\nu} \left( x e^{\frac{3\pi i}{4}} \right),$$ where $\mathrm{Re}$ denotes the real part of...")
 
 
(15 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
The $\mathrm{ber}_{\nu}$ function is defined as
 
The $\mathrm{ber}_{\nu}$ function is defined as
$$\mathrm{ber}(z)=\mathrm{Re} J_{\nu} \left( x e^{\frac{3\pi i}{4}} \right),$$
+
$$\mathrm{ber}_{\nu}(z)=\mathrm{Re} \hspace{2pt} J_{\nu} \left( z e^{\frac{3\pi i}{4}} \right),$$
where $\mathrm{Re}$ denotes the [[real part]] of a complex number and $J_{\nu}$ denotes the [[Bessel J sub nu|Bessel function of the first kind]].
+
where $\mathrm{Re}$ denotes the [[real part]] of a [[complex number]] and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
 +
 
 +
<div align="center">
 +
<gallery>
 +
File:Kelvinber,n=0plot.png|Graph of $\mathrm{ber}_0$.
 +
File:Kelvinber,n=0.5plot.png|Graph of $\mathrm{ber}_{\frac{1}{2}}$.
 +
File:Kelvinber,n=1plot.png|Graph of $\mathrm{ber}_1$.
 +
File:Kelvinber,n=2plot.png|Graph of $\mathrm{ber}_2$.
 +
File:Complexkelvinber,n=0plot.png|[[Domain coloring]] of $\mathrm{ber}_0$.
 +
File:Complexkelvinber,n=1plot.png|[[Domain coloring]] of $\mathrm{ber}_1$.
 +
</gallery>
 +
</div>
 +
 
 +
=References=
 +
* {{BookReference|Higher Transcendental Functions Volume II|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=findme|next=Kelvin bei}}: $\S 7.2.3 (19)$
 +
 
 +
[[Category:SpecialFunction]]
 +
 
 +
{{: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