双纽线｜w^2+c｜=1的弧长函数

FUNCTION OF THE ARC LENGTH OF THE LEMNISCATE |w 2+c|=1

设ｓ（ｃ）为双纽线｜ｗ２＋ｃ｜＝１的弧长，ｃ∈［０，＋∞）．本文证明了ｓ″（ｃ）＞０，ｃ∈（０，１）∪（１，＋∞）．最后。

Let s(c) be the arc length of the lemniscate |w 2+c|=1,c∈[0,+∞). In this paper we prove that s″(c)>0,c∈(0,1)∪(1,+∞), and we propose a problem of s (n) (c).