I mean that
$ K_{a} (x)= CJ_{a}(ix).$
Here $C$ is a complex number, and $a$ is real.
So is the Macdonald function a Bessel function in disguise (or proportional) of complex argument??
I mean that
$ K_{a} (x)= CJ_{a}(ix).$
Here $C$ is a complex number, and $a$ is real.
So is the Macdonald function a Bessel function in disguise (or proportional) of complex argument??
In fact $K_a(x) = \frac\pi2 i^{a+1} H^{(1)}_a(ix) = \frac\pi2 i^{a+1} [J_a(ix) + i Y_n(i x)]$ so it is closer related to the Hankel $H^{(1)}$ than to the Bessel function (of course the Hankel function is just a linear combination of the two Bessel functions $J$ and $Y$).