  A two-parameter sequence of orthogonal polynomials $\{P_n( x; \lambda,
t)\}_{n\ge 0}$ with respect to the weight function $x^\alpha e^{- \lambda x}
\rho_\nu(x t),\ \alpha > -1,\ \lambda, t \ge 0, \ \rho_{\nu}(x)= 2 x^{\nu/2}
K_\nu(2\sqrt x),\ x >0, \nu \ge 0$, where $K_\nu(z)$ is the modified Bessel
function, is investigated. The case $\lambda=0$ corresponds to the Prudnikov
polynomials and $t=0$ is related to the Laguerre polynomials. A special
one-parameter case $\{P_n( x; 1-t, t)\}_{n\ge 0},\ t \in [0,1]$ is analyzed as
well.
