Lǖroth误差和函数的若干性质

SOME PROPERTIES IN ERROR-SUMFUNCTION OF LǖROTH SERIES EXPANSION

本文研究了L櫣roth展式的误差和函数.利用误差和函数的PerronFrobenius算子,得到其积分值.最后,考察并获得其介值性定理,从而得出其图形是一个分形.

In this paper, we consider the error-sum function of Lüroth series expansion. By an application of the Perron-Frobenius operator on Lüroth series expansion, we get the integration of the error-sum function. At last, we investigate and obtain the intermediate value theorem on the error-sum function, as a consequence, we know its graph is a fractal.