Biorthogonal Polynomials and Numerical Integration Formulas for In nite Intervals

Date of Online Publication: 27/10/2007
Keywords: Biorthogonal polynomials; Orthogonal polynomials; Convergence acceleration; Numerical integration; Rational approximation
Authors: Avram Sidi, Doron S. Lubinsky
Pages: 209-226
In this work, we consider a class of numerical quadrature formulas for the infiniterange

integrals where being the Exponential Integral. These formulas are obtained by applying the Levin L and Sidi S transformations, two effective convergence acceleration methods, to the asymptotic expansions of and they turn out to interpolatory. In addition their abscissas turn out to have some interesting properties: For example if ,are the abscissas of the appropriate n-point formula, then the polynomial is orthogonal to some set of n real exponential function , where are the zeros of some known polynomials. We provide some tables and numerical examples that shown the effectiveness quadrature formulas.

 

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