1. Computations with half-range Chebyshev polynomials
- Author
-
B. Orel and Andrej Perne
- Subjects
Discrete mathematics ,Chebyshev polynomials ,Half-range Chebyshev polynomials ,Gegenbauer polynomials ,Orthogonal polynomials ,Applied Mathematics ,Discrete orthogonal polynomials ,Differentiation matrix ,Multiplication matrix ,Classical orthogonal polynomials ,Computational Mathematics ,symbols.namesake ,Wilson polynomials ,Hahn polynomials ,symbols ,Jacobi polynomials ,Three term recurrence relation ,Mathematics - Abstract
An efficient construction of two non-classical families of orthogonal polynomials is presented in the paper. The so-called half-range Chebyshev polynomials of the first and second kinds were first introduced by Huybrechs in Huybrechs (2010) [5]. Some properties of these polynomials are also shown. Every integrable function can be represented as an infinite series of sines and cosines of these polynomials, the so-called half-range Chebyshev–Fourier (HCF) series. The second part of the paper is devoted to the efficient computation of derivatives and multiplication of the truncated HCF series, where two matrices are constructed for this purpose: the differentiation and the multiplication matrix.
- Published
- 2012
- Full Text
- View/download PDF