On Bernstein's inequality for ultraspherical polynomials

被引：3

作者：

Alzer, H

机构：

[1] D-51545 Waldbröl

来源：

ARCHIV DER MATHEMATIK | 1997年 / 69卷 / 06期

关键词：

Ultraspherical Polynomial;

D O I：

10.1007/s000130050150

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the following inequality for the ultraspherical polynomials P-n((lambda)): (*) (sin(Theta))(lambda)\P-n((lambda))(cos(Theta))\<2(1-lambda) Gamma(n+3/2 lambda)/Gamma(lambda)Gamma(n+1+1/2 lambda), where 0 < lambda < 1,n greater than or equal to 0, and 0 < Theta < pi. Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia.

引用

页码：487 / 490

页数：4

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