Difference between revisions of "Kelvin kei"
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| − | File: | + | File:Complexkelvinkei,n=0plot.png|[[Domain coloring]] of $\mathrm{kei}_0$. |
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| + | =Properties= | ||
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| + | =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}} | {{:Kelvin functions footer}} | ||
[[Category:SpecialFunction]] | [[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): $\S 7.2.3 (20)$
