In a book titled 'Ordinary Differential Equations and Useful Polynomials', under the chapter 'Bessel's function', the author has introduced four new functions $\mathrm{ber}$, $\mathrm{bei}$, $\ker$, $\mathrm{kei}$ saying that
$\mathrm{ber}$, $\mathrm{bei}$ are Bessel real and Bessel imaginary functions. $\ker$, $\mathrm{kei}$ are their analogues.
The book provides enough information about $\mathrm{ber}$ and $\mathrm{bei}$, but there is not enough material about $\ker$ and $\mathrm{kei}$! (or, if there is, I'm not able to understand.) I completely understand about $\mathrm{ber}$/$\mathrm{bei}$ but concept is still not clear about $\ker$/$\mathrm{kei}$.
Any online reference is appreciated.