Kelvin ker

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 $K_{\nu}$.

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

References

• 1953: Harry Bateman: Higher Transcendental Functions Volume II ... (previous) ... (next): $\S 7.2.3 (19)$

Kelvin functions

Kelvin ber

Kelvin bei

Kelvin ker

Kelvin kei