A two-parameter family of orthogonal polynomials with respect to a Jacobi-type weight on the unit circle

[摘要] A two-parameter family of polynomials is introduced by a recursion formula. The polynomials are orthogonal on the unit circle with respect to the weight omega(alpha,beta)(theta) = \(1-z)(alpha)(1+z)(beta)\(2), alpha, beta > - 1/2, z = e(i theta). Explicit representation, norm estimates, shift identities, and explicit connection to Jacobi polynomials on the real interval [-1,1] is presented. (C) 1999 Academic Press.

[发布日期] 1999-12-15