求解析函数模最小零点的倒数幂级数法

The Method of Reciprocal Power Series for Finding the Modulus Mininum Zero Point of Analytic Function

解析函数ｆ（ｚ）的模最小零点满足一定条件时，可由［ｆ（ｚ）］－ １＝ ∞ｎ＝ ０ｂｎｚｎ 幂级数前后项系数比的序列｛ｂｎ／ｂｎ＋ １｝∞ｎ＝ ０所逼近．据此，得出求解析函数模最小零点的倒数幂级数法．

It is discussed when the modulus mininum zero point of the analytic function f(z) satisfies with given conditions,the sequence ｛ b n/b n+1 ｝ ∞ n=0 ,which is made up of coefficient ratio of the former and the latter term of the power series [f(z)] -1 ∞n=0b nz n, can convergent to the point.On this base,the method of reciprocal power series for finding modulus mininum zero point of analytic function is obtained.