On full equivalence logarithms of a sum and a maximal term of positive series of Taylor-Dirichlet type. (Ukrainian. English summary) Zbl 0948.30011
Summary: Conditions under which the asymptotic equality
\[
\ln F(\sigma)\sim\ln\max\{a_{n}\exp(\sigma\lambda_{n}+h(\sigma)\beta_{n}) \colon n\geq 0\}
\]
holds as \(\sigma\to+\infty\) for functional series of the form
\[
F(z)= \sum_{n=0}^{+\infty}a_{n}\exp\{\sigma\lambda_{n}+h(\sigma)\beta_{n}\}
\]
are proposed.
MSC:
| 30B50 | Dirichlet series, exponential series and other series in one complex variable |
