Difference between revisions of "General Dirichlet series"
From specialfunctionswiki
(Created page with "__NOTOC__ 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...") |
(→References) |
||
| Line 9: | Line 9: | ||
=References= | =References= | ||
| − | {{BookReference|The General Theory Of Dirichlet's Series|1915|G.H. Hardy|author2=Marcel Riesz|next=Dirichlet series}}: $I (1)$ (calls a general Dirichlet series a Dirichlet series of type $\lambda_k$) | + | {{BookReference|The General Theory Of Dirichlet's Series|1915|G.H. Hardy|author2=Marcel Riesz|next=Dirichlet series}}: $I.1.(1)$ (calls a general Dirichlet series a Dirichlet series of type $\lambda_k$) |
Latest revision as of 23:16, 17 March 2017
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
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 $\lambda_k$)
