一类亚纯函数的展式

Expansion of a sort of meromorphic function

用复分析中围道积分的计算方法,在复平面内适当选取积分路径和被积函数,由留数定理将亚纯函数πcscπz、πctgπz展开成亚纯函数项的级数,再根据亚纯函数项级数的解析性展开π2(cscπz)(ctgπz)及(πcscπz)2.

By making use of the calculating methods of a contour integral in complex plane, adequately choosing integral ways multiplicand function. meromorphic function πcscπz、πctgπz is expanded into aseries of meromorphic function. According to analytic of the series meromonphic function,(πcscπz)~2 and π~2(cscπz)(ctgπz) are expanded.