Let $L^\alpha_n(x)$ be Laguerre polynomials of type $n$. Assume $0<\beta<1$. Is there a closed formula for this sum $$\sum^\infty_{j=0} \frac{1}{(b+j)^{1-\beta}}L^{m}_j(x)$$

where $b>0$ and $m\in \Bbb N$

Thank you in advance