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Resumen de Uniform Estimates of Ultraspherical Polynomials of Large Order

Laura De Carli

  • In this paper we prove the sharp inequality |Pn(s)(x)| = Pn(s)(1) (|x|n + {n-1}/{2 s+1} (1 - |x|n)), where Pn(s)(x) is the classical ultraspherical polynomial of degree n and order s = n frac{1 + v 5}{4}. This inequality can be refined in [0, zns] and [zns, 1], where zns denotes the largest zero of Pn(s) (x).


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