Abstract
In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of 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.
Acknowledgment
The author wishes to thank Francesca Aicardi for her helpful tips on the presentation.
Additional information
Notes on contributors
Lorenzo David
LORENZO DAVID is a high school student who learned calculus as autodidact during 2020’s first Covid-19 lockdown.