Difference between revisions of "Sum of values of sinc"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\displaystyle\sum_{k=1}^{\infty} \mathr...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\displaystyle\sum_{k=1}^{\infty} \mathrm{sinc}(k) = \dfrac{\pi-1}{2},$$ | $$\displaystyle\sum_{k=1}^{\infty} \mathrm{sinc}(k) = \dfrac{\pi-1}{2},$$ | ||
| − | where $\mathrm{sinc}$ denotes the [[sinc|$\mathrm{sinc}$]] function and $\pi$ denotes [[ | + | where $\mathrm{sinc}$ denotes the [[sinc|$\mathrm{sinc}$]] function and $\pi$ denotes [[pi]]. |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 08:02, 8 June 2016
Theorem
The following formula holds: $$\displaystyle\sum_{k=1}^{\infty} \mathrm{sinc}(k) = \dfrac{\pi-1}{2},$$ where $\mathrm{sinc}$ denotes the $\mathrm{sinc}$ function and $\pi$ denotes pi.
