Formula:238

Digital Library of Mathematical Functions ID 1.8.E14

${\displaystyle{\displaystyle\sum^{\infty}_{n=-\infty}f(x+n)=\sum^{\infty}_{n=-\infty}e^{2\pi inx}\int^{\infty}_{-\infty}f(t)e^{-2\pi int}\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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