Generalized binomials in fractional calculus
Combinatorics
2020-10-13 v1
Abstract
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities, including an adapted version of the Pascal's rule. We then investigate the associated generating functions, for which we establish a recursive, combinatorial and integral formulation. From this, we derive an asymptotic version of the Binomial Theorem. A combinatorial and asymptotic analysis of some finite sums completes the paper.
Cite
@article{arxiv.2010.05610,
title = {Generalized binomials in fractional calculus},
author = {Mirko D'Ovidio and Anna Chiara Lai and Paola Loreti},
journal= {arXiv preprint arXiv:2010.05610},
year = {2020}
}