Clausen sine

From specialfunctionswiki
Revision as of 19:44, 7 September 2020 by Tom (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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.

Properties

See also

Clausen cosine

References