Numerical studies of the Möbius power series

We define the Möbius power series throughf(z)=Σn-1∞zn,g(z)=Σn=1∞μ(n)zn/n where μ(n) is the usual Möbius function. This paper presents some heuristic estimates describing the behavior off(z) andg(z) when |z| is close to 1 together with representations in terms of elementary functions for real values ofz. Function tables are also given together with zeros and a few other special values.