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