Difference between revisions of "Sum of values of sinc"
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The following formula holds: | 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== | ==Proof== | ||
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.
