Szeg\"o kernels and asymptotic expansions for Legendre polynomials
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🧮 math.CA
math.CV
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asymptoticexpansionslegendrepolynomialsszegapproachasymptoticscomplete
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We present a geometric approach to the asymptotics of the Legendre polynomials $P_{k,n+1}$, based on the Szeg\"o kernel of the Fermat quadric hypersurface, and leading to complete asymptotic expansions holding on expanding subintervals of $[-1,1]$.
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