Is a Mac donald function really a Bessel function

[zetafunction]

my question is if a Mac Donald function is really a Bessel function i mean

$$J_{a}(ix)= CK_{a}(x)$$

here 'C' is a complex number

 

[lurflurf]

As far as I know a Mac Donald function is the same as a modified Bessel function of the second kind

 

[JJacquelin]

The modified Bessel functions of the second kind of imaginary argument (or the Bessel functions of the third kind) are alternatively named Basset functions , Macdonald functions, or modified Hankel functions.