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Discrete (Legendre) orthogonal polynomials—a survey
Author(s) -
Neuman C. P.,
Schonbach D. I.
Publication year - 1974
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620080406
Subject(s) - orthogonal polynomials , discrete orthogonal polynomials , legendre polynomials , mathematics , classical orthogonal polynomials , gegenbauer polynomials , hahn polynomials , kravchuk polynomials , jacobi polynomials , mehler–heine formula , wilson polynomials , normalization (sociology) , difference polynomials , pure mathematics , algebra over a field , discrete mathematics , mathematical analysis , sociology , anthropology
The discrete (Legendre) orthogonal polynomials , (DLOP's) are useful for approximation purposes. This set of m th degree polynomials { P m ( K , N )} are orthogonal with unity weight over a uniform discrete interval and are completely determined by the normalization P m (O, N ) = 1. The authors are employing these polynomials as assumed modes in engineering applications of weighted residual methods. Since extensive material on these discrete orthogonal polynomials, and their properties, is not readily available, this paper is designed to unify and summarize the presently available information on the DLOP's and related polynomials. In so doing, many new properties have been derived. These properties, along with sketches of their derivation, are included. Also presented are a representation of the DLOP's as a product of vectors and matrices, and an efficient computational scheme for generating these polynomials.