The generalized-Euler-constant function $\gamma (z)$ and a generalization of Somos's quadratic recurrence constant

Jonathan Sondow, Petros Hadjicostas

We define the generalized-Euler-constant function $\gamma (z)={\sum }_{n=1}^{\infty }{z}^{n-1}(\frac{1}{n}-\log \frac{n+1}{n})$ when $|z|\le 1$. Its values include both Euler's constant $γ=…