Difference between revisions of "Kelvin kei"
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(Created page with "The $\mathrm{bei}_{\nu}$ function is defined as $$\mathrm{ber}(z)=\mathrm{Im} \hspace{2pt} K_{\nu} \left( x e^{\frac{\pi i}{4}} \right),$$ where $\mathrm{Im}$ denotes the im...") |
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| − | The $\mathrm{ | + | The $\mathrm{kei}_{\nu}$ function is defined as |
| − | $$\mathrm{ | + | $$\mathrm{kei}_{\nu}(z)=\mathrm{Im} \left[ e^{-\frac{\nu \pi i}{2}} K_{\nu} \left( z e^{\frac{\pi i}{4}} \right) \right],$$ |
where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $K_{\nu}$ denotes the [[Modified Bessel K sub nu|modified Bessel $K_{\nu}$]]. | where $\mathrm{Im}$ denotes the [[imaginary part]] of a [[complex number]] and $K_{\nu}$ denotes the [[Modified Bessel K sub nu|modified Bessel $K_{\nu}$]]. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Complexkelvinkei,n=0plot.png|[[Domain coloring]] of $\mathrm{kei}_0$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Properties= | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Higher Transcendental Functions Volume II|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Kelvin ker|next=findme}}: $\S 7.2.3 (20)$ | ||
| + | |||
| + | {{:Kelvin functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 05:42, 4 March 2018
The $\mathrm{kei}_{\nu}$ function is defined as $$\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 $K_{\nu}$.
Domain coloring of $\mathrm{kei}_0$.
Properties
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume II ... (previous) ... (next): $\S 7.2.3 (20)$
