Series representation of multiplication of two Bessel function $J_{\mu}(az) J_{\nu}(bz)$ is in terms of sum of hypergeometric functions $_2F_1$, it given in book Treatise on Theory of Bessel Functions by Watson.

What is representation of multiplication of two modified Bessel function of different kinds

$I_{\mu}(az) K_{\nu}(bz) = ?$

Interesting to me is case of $\nu$ is an integer $n$.