留数定理在三角和恒等式中的一个应用

Application of the Residue Theorem to Trigonometric Sum Identities

中文关键词:  留数定理  三角函数  围道积分.

英文关键词:residue theorem  trigonometric function  contour integration.

中文摘要:

      通过使用柯西留数定理计算围道积分,证明了含有参变量的一般化的三角函数求和公式.可以看到,其中包含了若干已知的三角和恒等式作为特例.

英文摘要:

      By evaluating a contour integral with the Cauchy residue theorem, we prove a general summation formula on trigonometric sum, which contains several interesting trigonometric identities as special cases.