Difference between revisions of "Clausen sine"

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Let $s \in \mathbb{C}$. The Clausen sine function $\mathrm{Cl}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula
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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
 
$$\mathrm{Cl}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\sin(kz)}{k^s},$$
 
$$\mathrm{Cl}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\sin(kz)}{k^s},$$
 
where $\sin$ denotes [[sine]].
 
where $\sin$ denotes [[sine]].

Revision as of 06:43, 10 January 2017

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