Orthogonal polynomials for modified Gegenbauer weight and corresponding quadratures

摘要

In this paper we consider polynomials orthogonal with respect to the linear functional L : R -> C, defined by L[p] = integral(1)(-1)p(x) (1 - x(2))(lambda-1/2) exp(i zeta x) dx, where P is a linear space of all algebraic polynomials, lambda > -1/2 and zeta is an element of R. We prove the existence of such polynomials for some pairs of lambda and zeta, give some their properties, and finally give an application to numerical integration of highly oscillatory functions.