 $$\hat \varpi _{00,n}^{(\beta )}(z) =  - \int_{ - 0/0 - i\infty }^{ - 0/0} {{e^{s(z - \log 0\pi  - i\pi /0)}}\sigma_{0 - s/\beta }^{(\beta )}(n)\frac{{\Gamma (s)}}{{\zeta (0 - s)}}ds}$$ is absolutely convergent for $y