General Dirichlet series

In the field of mathematical analysis, a general Dirichlet series is an infinite series that takes the form of

where ${\displaystyle a_{n}}$, ${\displaystyle s}$ are complex numbers and ${\displaystyle \{\lambda _{n}\}}$ is a strictly increasing sequence of nonnegative real numbers that tends to infinity.

A simple observation shows that an 'ordinary' Dirichlet series

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