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arXiv · 2005.12363

The Binomial Coefficient as an (In)finite Sum of Sinc Functions

Lorenzo David
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Abstract

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the product of the binomial coefficient and a given function, which, in some cases, turns out to be equal to the series of their values on the integers. Finally, we establish a list of identities obtained by applying these formulas.

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Lorenzo David. 2020-05-22. The Binomial Coefficient as an (In)finite Sum of Sinc Functions. https://arxiv.org/abs/2005.12363

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