Kelvin kei

The $\mathrm{kei}_{\nu}$ function is defined as $$\mathrm{kei}(z)=\mathrm{Im} e^{-\frac{\nu \pi i}{2}} \hspace{2pt} K_{\nu} \left( z e^{\frac{\pi i}{4}} \right),$$ where $\mathrm{Im}$ denotes the imaginary part of a complex number and $K_{\nu}$ denotes the modified Bessel $K_{\nu}$.

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  Domain coloring of $\mathrm{kei}_0$.