Kelvin kei
From specialfunctionswiki
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): $\S 7.2.3 (20)$
