ACTA issues

Asymptotics for orthogonal polynomials with respect to the Laguerre measure modified by a rational factor

Bujar Xh. Fejzullahu

Acta Sci. Math. (Szeged) 77:1-2(2011), 73-85

Abstract. In this paper we study the asymptotic properties of the polynomials orthogonal with respect to the modified Laguerre weight ${\prod_{k=1}^K(x-a_k)^{N_k}\over\prod _{j=1}^M(x-\eta_j)} x^\alpha e^{-x},$ where $N_k\in{\msbm N},$ $a_k,\eta_j< 0$ and $\eta_k\not=\eta_l$ for $k\not=l.$

AMS Subject Classification (1991): 33C45, 42C05

Keyword(s): orthogonal polynomials, modified Laguerre-type orthogonal polynomials, asymptotics

Received September 8, 2009, and in final form December 14, 2009. (Registered under 103/2009.)