Wang, Chunjie The arc length of the lemniscate \(| w^2+c|=1\). (Chinese. English summary) Zbl 0926.31001 Acta Math. Sci. (Chin. Ed.) 18, No. 3, 297-301 (1998). Summary: Let \(s(c)\) be the arc length of the lemniscate \(| w^2+c|=1\), \(c\in [0,+\infty)\). The author discusses some properties of the function \(s(c)\), and solves the case \(n=2\) of a conjecture proposed by P. Erdős, F. Herzog and B. Piranian [J. Anal. Math. 6, 125–148 (1958; Zbl 0088.25302)]. Cited in 1 Document MSC: 31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions 30B10 Power series (including lacunary series) in one complex variable 30C85 Capacity and harmonic measure in the complex plane Keywords:arc length; lemniscate; power series; binomial coefficients Citations:Zbl 0821.31002; Zbl 0088.25302 PDFBibTeX XMLCite \textit{C. Wang}, Acta Math. Sci. (Chin. Ed.) 18, No. 3, 297--301 (1998; Zbl 0926.31001)