Numerical studies of the Möbius power series

We define the Möbius power series throughf(z)=_n-1zⁿ,g(z)=_n=1(n)zⁿ/n where (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.