Formula:649

Digital Library of Mathematical Functions ID 1.17.E20

${\displaystyle{\displaystyle\delta_{n}\left(x-a\right)=\frac{1}{2\pi}\sum_{k=-n}^{n}e^{ik(x-a)}\left(=\frac{\sin\left((n+\frac{1}{2})(x-a)\right)}{2\pi\sin\left(\frac{1}{2}(x-a)\right)}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\delta_{n}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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