New and old sequences of orthogonal polynomials

Authors:
Maitree Podisuk;Pornchai Chaisanit;Netchanok Kongchouy
Affiliations:
Department of Mathematics and Computer Science, King Mongkut's Institute of Tecnology Chaokhuntaharn Ladkrabang, Ladkrabang, Bangkok, Thailand;Department of Mathematics and Computer Science, King Mongkut's Institute of Tecnology Chaokhuntaharn Ladkrabang, Ladkrabang, Bangkok, Thailand;Department of Mathematics and Statistics, Payap University, Chiang Mai, Thailand
Venue:
MMACTEE'06 Proceedings of the 8th WSEAS international conference on Mathematical methods and computational techniques in electrical engineering
Year:
2006

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Abstract

In this paper, two sequences of orthogonal polynomials on the closed interval [0,1] with respect to the weight function w(x) = 1 + sin (1/x) and w(x) = 1 + cos (1/x) which were given by Walter Gautschi [3] in 2004 and four new sequences of orthogonal polynomials on the closed interval [0,1] with respect to the weight function, w(x) = ln (1+x), w(x) = (1/(1+x), w(x) = 1+x and w(x) = 1-(x) = 1-x will be introduced. We will show these orthogonal polynomials up to degree seven of each type of orthogonal polynomials. The Gauss-Quadrature formulas of all six sequences of orthogonal polynomials will be presented. One example will be shown.