Sinc sum

From: Kaba <none@xxxxxxxx>
Date: Thu, 28 Feb 2008 02:10:40 +0200

Let
sinc(x) = sin(pi * x) / (pi * x)

Does it hold that
for all x in [0, 1[ in R: sum[i in Z] sinc(x + i) = 1
?

I'd expect yes. How to prove it?

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