tailieunhanh - báo cáo hóa học:" Research Article Derivatives of Orthonormal Polynomials and ´ Coefficients of Hermite-Fejer Interpolation "

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Derivatives of Orthonormal Polynomials and ´ Coefficients of Hermite-Fejer Interpolation | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 816363 29 pages doi 2010 816363 Research Article Derivatives of Orthonormal Polynomials and Coefficients of Hermite-Fejer Interpolation Polynomials with Exponential-Type Weights H. S. Jung1 and R. Sakai2 1 Department of Mathematics Education Sungkyunkwan University Seoul 110-745 South Korea 2 Department of Mathematics Meijo University Nagoya 468-8502 Japan Correspondence should be addressed to H. S. Jung hsun90@ Received 10 November 2009 Accepted 14 January 2010 Academic Editor Vijay Gupta Copyright 2010 H. S. Jung and R. Sakai. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Let R -TO to and let Q e C2 R 0 to be an even function. In this paper we consider the exponential-type weights Wp x x p exp -Q x p -1 2 x e R and the orthonormal polynomials pn wp x of degree n with respect to Wp x . So we obtain a certain differential equation of higher order with respect to pn wp x and we estimate the higher-order derivatives of pn wp x and the coefficients of the higher-order Hermite-Fejer interpolation polynomial based at the zeros of pn wp x . 1. Introduction Let R -TO to and R 0 to . Let Q e C2 R R be an even function and let w x exp -Q x be such that fTOxnw2 x dx TO for all n 0 1 2 . For p -1 2 we set wp x x pw x x e R. Then we can construct the orthonormal polynomials pn p x pn wp x of degree n with respect to wp x . That is TO pn p x pm p x w2 x dx ỗmn Kronecker s delta -TO Pn p x Ynxn Yn fn p 0. 2 Journal of Inequalities and Applications We denote the zeros of pn p x by to xn n p xn-1 n p x2 n p x1 n p TO. A function f R R is said to be quasi-increasing if there exists C 0 such that f x Cf y for 0 x y. For any two sequences bn TO 1 and cn TO 1 of nonzero real numbers or functions we .