ON POLYNOMIALS ORTHOGONAL ON THE SEMICIRCLE AND APPLICATIONS

[摘要] Polynomials {pi(n)} orthogonal on the semicircle GAMMA = {z is-an-element-of C: z = e(itheta), 0 less-than-or-equal-to 0 less-than-or-equal-to pi} with respect to the inner product (f, g) = integral(GAMMA)f(z)g(z)w(z)(iz)-1 dz, where z --> w(z) is a complex weight function, have been introduced in 1986-1987 by Gautschi, Landau and the author. In this paper we introduce the functions of the second kind, as well as the corresponding associated polynomials, and prove some recurrence relations. For Gauss-Gegenbauer quadrature formulae over the semicircle, applied to analytic functions, we develop error bounds from contour integral representations of the remainder term and give some numerical results.

[发布日期] 1993-12-31

[关键词] COMPLEX ORTHOGONAL POLYNOMIALS;RECURRENCE RELATIONS;NUMERICAL INTEGRATION;ERROR BOUND