Difference between revisions of "Clausen sine"
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| − | File:Clausensine0. | + | File:Clausensine0.5.png|Graph of $\mathrm{Cl}_{0.5}$. |
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Latest revision as of 19:44, 7 September 2020
Let $s \in \mathbb{C}$. The Clausen sine function $\mathrm{Cl}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined as the analytic continuation of the series $$\mathrm{Cl}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\sin(kz)}{k^s},$$ where $\sin$ denotes sine.
Graph of $\mathrm{Cl}_{0.5}$.
