Lobachevsky’s integral formula

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Let f be an even function with period π. Then the following remarkable theorem by Lobachevsky holds.

This theorem is useful in Fourier analysis and signal processing. It’s useful to know even in the special case f(x) = 1.

For a "jinc" analog, see this paper.

Every time I see the name Lobachevsky I think of Tom Lehrer’s song about him. You can find the words here and the audio here.

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