Laurent expansion of Dirichlet series. II (Q1084217)

[For part I see the author in Bull. Aust. Math. Soc. 33, 351-357 (1986; Zbl 0578.30003).] Let \(f(s)=\sum b_ na_ n^{-s}\) be a Dirichlet series, with appropriate conditions on \(a_ n\) and \(b_ n\), convergent in Re s\(>\lambda\) (\(\geq 1)\) and having an analytic continuation at least in Re s\(>0\) with a possible pole at \(s=\lambda\). Suppose \(f(\sigma +it)\) grows slower than a convenient power of t as \(t\to \infty\), we obtain the Laurent coefficients in the expansion of f(s) at \(s=\lambda\). The conditions mentioned above are general enough to cover a good class of Dirichlet series.