Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product

Abstract: Let be a finite positive Borel measure supported on and introduce the discrete Sobolev-type inner productwhere the mass points belong to , and . In this paper, we obtain generalized trace formula and asymptotics of the averaged Turan determinant for the Sobolev-type orthogonal polynomials. Asymptotics of the recurrence coefficients for symmetric Gegenbauer–Sobolev orthogonal polynomials is obtained. Trace formula and asymptotics of Turan''s determinant for Gegenbauer–Sobolev orthogonal polynomials are also given. [Copyright &y& Elsevier]