Formula:239

Digital Library of Mathematical Functions ID 1.8.E15

${\displaystyle{\displaystyle\tfrac{1}{2}f(0)+\sum^{\infty}_{n=1}f(n)=\int^{\infty}_{0}f(x)\mathrm{d}x+2\sum^{\infty}_{n=1}\int^{\infty}_{0}f(x)\cos\left(2\pi nx\right)\mathrm{d}x.}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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