Abstract
We study the uniform asymptotics for the orthogonal polynomials with respect to weights composed of both absolutely continuous measure and discrete measure, by taking a special class of the sieved Pollaczek polynomials as an example. The Plancherel–Rotach type asymptotics of the sieved Pollaczek polynomials are obtained in the whole complex plane. The Riemann–Hilbert method is applied to derive the results. A main feature of the treatment is the appearance of a new band consisting of two adjacent intervals, one of which is a portion of the support of the absolutely continuous measure, the other is the discrete band.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
