Laguerre projection kernel

For $w(x)=x^a{e}^{-x}$ on $[0,\infty )$, $a>-1$, the monic Generalized Laguerre polynomials have squared norms $h_j=j!\Gamma (j+a+1)$. The corresponding orthogonal polynomial projection kernel is $(xy{)}^{a/2}{e}^{-(x+y)/2}{\sum }_{j=0}^{m-1}j!L_j^{(a)}(x)L_j^{(a)}(y)/\Gamma (j+a+1)$ for nonnegative $x,y$, and zero otherwise.