Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights (Q1977417)

The author proves uniform asymptotic formulae when \(n\to\infty\) on the unit circle for derivatives of (complex) orthogonal polynomials based on Jacobi-type weights with a finite number of power type singularities. The corollaries of these results settle the corresponding problems for generalized Jacobi polynomials on \([-1, 1]\), that is, for the (real) orthogonal polynomials based on power type weights with inner singularities. The results are based on the works of \textit{G. Szegő} [``Orthogonal polynomials'' (1939; Zbl 0023.21505) ] and \textit{V. M. Badkov} [Proc. Steklov Inst. Math. 198, 37-82 (1994; Zbl 0824.42020)].