Kelvin kei

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 $K_{\nu}$.