Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

Milovanovic, Gradimir V., and Cvetkovic, Aleksandar S.. "Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type." Mathematica Balkanica New Series 26.1-2 (2012): 169-184. <http://eudml.org/doc/281518>.

@article{Milovanovic2012,
abstract = {MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems with strong nonclassical weights on (0;+1), including a conjecture for an oscillatory weight on [¡1; 1]. Finally, we give some new results on orthogonal polynomials on radial rays in the complex plane.},
author = {Milovanovic, Gradimir V., Cvetkovic, Aleksandar S.},
journal = {Mathematica Balkanica New Series},
keywords = {orthogonal polynomials; weight function; measure; moments; three-term recurrence relation; Gaussian quadratures; nodes; weights; software},
language = {eng},
number = {1-2},
pages = {169-184},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type},
url = {http://eudml.org/doc/281518},
volume = {26},
year = {2012},
}

TY - JOUR
AU - Milovanovic, Gradimir V.
AU - Cvetkovic, Aleksandar S.
TI - Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
JO - Mathematica Balkanica New Series
PY - 2012
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 26
IS - 1-2
SP - 169
EP - 184
AB - MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems with strong nonclassical weights on (0;+1), including a conjecture for an oscillatory weight on [¡1; 1]. Finally, we give some new results on orthogonal polynomials on radial rays in the complex plane.
LA - eng
KW - orthogonal polynomials; weight function; measure; moments; three-term recurrence relation; Gaussian quadratures; nodes; weights; software
UR - http://eudml.org/doc/281518
ER -