Kragujevac J. Math. 26 (2004) 39–48. S–ORTHOGONALITY ON THE SEMICIRCLE1

Abstract. In this paper s–orthogonal polynomials on the semicircle are considered. Gener-alizing the previous works of Gautschi, Milovanovic ́ and Landau [5, 4, 8, 7, 9, 3] we transfer concept of s–orthogonality (see [6, 10]) to the unit semicircle in the complex plane, with respect to the complex-valued inner product (f, g) = ∫ pi 0 f(e iθ)g(eiθ)w(eiθ) dθ. A detailed study is made of the s–orthogonal polynomials on the semicircle in the case of the Chebyshev weight of the first kind. 1