Uniform Estimates of Ultraspherical Polynomials of Large Order

• Autores: Laura De Carli
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 3, 2005, págs. 382-393
• Idioma: inglés
• DOI: 10.4153/cmb-2005-035-2
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• Resumen

  • 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).