2020/05/22 by David, Lorenzo
#11B65 #33B15 #FOS: Mathematics #History and Overview (math.HO)
paper · doi:10.48550/arxiv.2005.12363
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.