\begin{definition}[Definition:General Dirichlet Series]
Let $a_n$ be a sequence in $\C$.
Let $\sequence {\lambda_n}$ be a strictly increasing sequence of non-negative real numbers whose limit is infinity.
A '''general Dirichlet series of type $\lambda_n$''' is a complex function $f: \C \to \C$ defined by the series:
:$\ds \map f s = \sum_{n \mathop = 1}^\infty a_n e^{-\lambda_n s}$
which is defined at the points where it converges.
\end{definition}