STRONG ASYMPTOTICS AND THE ASYMPTOTIC ZERO DISTRIBUTIONS OF LAGUERRE POLYNOMIALS Ln(an+α) AND HERMITE POLYNOMIALS Ηn(an+α)
QueAtioni oi con&tnained on. weighted polynomial approximation an.e clo&ely related to orthogonal polynomials with degree dependent weight functions, and various of it& asymptotic. properties. Supplementing earlier and recent re&ulti strong asymptotia ion. the. generalized Laguerre and Hermite polynomials L^^(z), H^\z) axe derived, thai iL· asymptotic ionmi i f , ζ is in the interval oi zeros, [rn> sn] say, and ii ζ belongs to the cut plane $ [rn> sn]. Thereby in particular generali.zatU.oni o{ the classical Planchenel-Rotach iormulae aAe established and the limit distribution oi the zeros is computed as the degn.ee η tend!) to infinity. AMS 1980 subject classification: 30 C 15, 33 A 65.