Szegö kernels and asymptotic expansions for Legendre polynomials

Abstract

We present a geometric approach to the asymptotics of the Legendre polynomials $P_{k,n+1}$, based on the Szegö kernel of the Fermat quadric hypersurface, and leading to complete asymptotic expansions holding on expanding subintervals of $[-1,1]$.

Cited by in corpus (1)

• Gaussian integrals depending by a quantum parameter in finite dimension