On the $L^2$-norm of Gegenbauer polynomials

Abstract

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

7 pages. The power of the rest term in Corollary 1.4 was wrong as stated and has been corrected. Also, Corollary 1.4 was extended, and its proof streamlined. My email was added and the acknowledgment was modified. A minor typo was corrected, a reference updated

References in corpus (1)

• Approximation to uniform distribution in SO(3)