On the L 2 -norm of Gegenbauer polynomials

Math Sci (Karaj). 2022;16(2):115-119. doi: 10.1007/s40096-021-00398-1. Epub 2021 Apr 21.

Abstract

Gegenbauer, also known as ultra-spherical, polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula for and compute the asymptotic behavior of their L 2 -norm.

Keywords: L 2 -norm; Asymptotics; Gegenbauer polynomials.