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 | ||
$$\mathrm{bei}_{\nu}(z)=\mathrm{Im} \hspace{2pt} J_{\nu} \left( z e^{\frac{3\pi i}{4}} \right),$$ | $$\mathrm{bei}_{\nu}(z)=\mathrm{Im} \hspace{2pt} J_{\nu} \left( z e^{\frac{3\pi i}{4}} \right),$$ | ||
| − | where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $J_{\nu}$ denotes the [[Bessel J | + | 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: | + | 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> | ||
| − | + | =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.
Graph of $\mathrm{bei}_0$.
Graph of $\mathrm{bei}_1$.
Domain coloring of $\mathrm{bei}_0$.
Domain coloring of $\mathrm{bei}_1$.
Properties
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume II ... (previous) ... (next): $\S 7.2.3 (19)$
