Derivatives of Orthonormal Polynomials and Coefficients of Hermite-Fejer Interpolation Polynomials with Exponential-Type Weights

作者：Jung H S^*; Sakai R

来源：Journal of Inequalities and Applications, 2010, 816363.

DOI：10.1155/2010/816363

Let R = (-infinity, infinity), and let Q is an element of C(2) : R -> [0, infinity) be an even function. In this paper, we consider the exponential-type weights w(rho)(x) = |x|(rho) exp(-Q(x)), rho > -1/2, x is an element of R, and the orthonormal polynomials p(n)(w(rho)(2);x) of degree n with respect to w(rho)(x). So, we obtain a certain differential equation of higher order with respect to p(n)(w(rho)(2);x) and we estimate the higher-order derivatives of p(n)(w(rho)(2);x) and the coefficients of the higher-order Hermite-Fejer interpolation polynomial based at the zeros of p(n)(w(rho)(2);x).

• 出版日期2010