Zeckendorf expansion, Dirichlet series and infinite series involving the infinite Fibonacci word

Shuo Li

Let $\beta =\frac{1+\sqrt{5}}{2}$, $(a_n{)}_{n\in {\mathbb{N}}^{+}}$ be a non-uniform morphic sequence involving the infinite Fibonacci word and $(\delta (n){)}_{n\in {\mathbb{N}}^{+}}$ be a positive s…