A BOUND ON THE LAGUERRE-POLYNOMIALS

We give the following bounds on Laguerre polynomials and their derivatives (alpha greater-than-or-equal-to 0): [GRAPHICS] for all natural numbers k,p,n greater-than-or-equal-to 0 and t greater-than-or-equal-to 0. Also, we give (as the main result of this paper) a technique to estimate the order in k and p in bounds similar to the previous ones, which will be used to see that the estimate on k and p in the previous bounds is sharp and to give an estimate on k and p in other bounds on the Laguerre polynomials proved by Szego.