General Dirichlet series

From specialfunctionswiki
Revision as of 23:16, 17 March 2017 by Tom (talk | contribs) (References)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Let $z \in \mathbb{C}$ and let $\lambda_k \in \mathbb{R}$ for $k \in \{0,1,2\ldots\}$ be so that $\lambda_{k} < \lambda_{k+1}$ and $\displaystyle\lim_{k \rightarrow \infty} \lambda_k=\infty$. A general Dirichlet series is a series of the form $$\displaystyle\sum_{k=1}^{\infty} a_k e^{-\lambda_k z}.$$

Properties

See Also

Dirichlet series

References

1915: G.H. Hardy and Marcel Riesz: The General Theory Of Dirichlet's Series ... (next): $I.1.(1)$ (calls a general Dirichlet series a Dirichlet series of type $\lambda_k$)