付氏变换在三角级数求和中的应用

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Summation of Trigonometric Series By Fourier Transforms

Shanghai University of Technology; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要: 本文建立了用付氏变换在三角级数求和中的新的重要定理,并用付氏变换的已知结果,解决了不少困难和复杂的三角级数求和问题.这是三角级数求和的新方法,作者曾用以编著了数以万计的三角级数之和的大表.许多结果都是新的.

Abstract: This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms.By means of the known results of Fourier transforms,many difficult and complex problems of summation of trigonometric series can be solved.This method is a comparatively unusual way to find the summation of trigonometric series,and has been used to establish the comprehensive table of summation of trigonometric series.In this table 10 thousand scries arc given,and most of them are new.

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