Difference between revisions of "Clausen cosine"
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(Created page with "Let $s \in \mathbb{C}$. The Clausen cosine function $\tilde{\mathrm{Cl}}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\tilde{\mathrm{Cl}}_s(z)=\displaystyle\su...") |
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| − | Let $s \in \mathbb{C}$. The Clausen cosine function $\tilde{\mathrm{Cl}}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined | + | Let $s \in \mathbb{C}$. The Clausen cosine function $\tilde{\mathrm{Cl}}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined as the [[analytic continuation]] of the series |
$$\tilde{\mathrm{Cl}}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\cos(kz)}{k^s},$$ | $$\tilde{\mathrm{Cl}}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\cos(kz)}{k^s},$$ | ||
where $\cos$ denotes [[cosine]]. | where $\cos$ denotes [[cosine]]. | ||
Revision as of 06:43, 10 January 2017
Let $s \in \mathbb{C}$. The Clausen cosine function $\tilde{\mathrm{Cl}}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined as the analytic continuation of the series $$\tilde{\mathrm{Cl}}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\cos(kz)}{k^s},$$ where $\cos$ denotes cosine.
