一类三角级数的和函数计算

The Sum Functions of a Trigonometric Series

本文利用一些技巧性的手段构造出部分和S_n的方程,进而解出S_n,再根据函数项级数的和函数定义,求得了三角级数∑n=1∞cosnx/q^n(q>1)和∑n=1∞sinnx/q^n(q>1)的和函数表达式。

By using a skillful method,the author constructs the equation of a partial sum S_n,and works out the equation of S_n.Then according to the sum functions definition of the series of functions,the author works out the sum functions expression of the series of trigono-∞∞cosnx metric ∑n=1∞cosnx/q^n（q1）and∑n=1∞sinnx/q^n（q1）.