Polynomial approximation with Pollaczeck-Laguerre weights on the real semiaxis. A survey

Electronic Transactions on Numerical Analysis

Giuseppe Mastroianni¹ 

关键词: orthogonal polynomials;    weighted polynomial approximation;    polynomial inequalities;    Gaussian quadrature rules;    Lagrange interpolation;    Pollaczeck-Laguerre exponential weights;   

DOI  :  

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

This paper summarizes recent results on weighted polynomial approximations for functions defined on the real semiaxis. The function may grow exponentially both at 0 and at +∞. We discuss orthogonal polynomials, polynomial inequalities, function spaces with new moduli of smoothness, estimates for the best approximation, Gaussian rules, and Lagrange interpolation with respect to the weight w(x)=xγe−x−α−xβ (α>0, β>1, γ≥0).

【 授权许可】

Unknown