Estimates for the norms of products of sines and cosines

被引：5

作者：

Bell, Jordan ^{[1
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 1A1, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 405卷 / 02期

关键词：

Trigonometric polynomials; Pentagonal number theorem; q-series; Integer partitions; Catalan's constant; PARTITION; POLYNOMIALS; ZEROS;

D O I：

10.1016/j.jmaa.2013.04.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove asymptotic formulas for the L-p norms of P-n(theta) = Pi(n)(k=1)(1 - e(ik theta)) and Q(n)(theta) = Pi(n)(k=1) (1 + e(ik theta)). These products can be expressed using Pi(n)(k=1) sin(k theta/2) and Pi(n)(k=1) cos(k theta/2) respectively. We prove an estimate for P-n at a point near where its maximum occurs. Finally, we give an asymptotic formula for the maximum of the Fourier coefficients of Q(n). (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：530 / 545

页数：16

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