论文标题
二项式系数作为（in）有限的SINC函数总和
The Binomial Coefficient as an (In)finite Sum of Sinc Functions
论文作者
论文摘要
在本文中，我们给出了将二项式系数概括为复数的公式，作为$ \ sinc $函数的线性组合。然后，我们给出一个通用公式，以计算二项式系数和给定函数乘积的实际线的积分，在某些情况下，该组合与整数上的一系列值相等。最后，我们建立了通过应用这些公式获得的身份列表。
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.
