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Journal of Complex Analysis
Volume 2017 (2017), Article ID 7823545, 13 pages
https://doi.org/10.1155/2017/7823545
Research Article

Szegö Kernels and Asymptotic Expansions for Legendre Polynomials

Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy

Correspondence should be addressed to Roberto Paoletti

Received 16 July 2017; Accepted 24 September 2017; Published 31 October 2017

Academic Editor: Sergei Grudsky

Copyright © 2017 Roberto Paoletti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a geometric approach to the asymptotics of the Legendre polynomials , based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of .