论文标题
分数演算中的广义二项式
Generalized binomials in fractional calculus
论文作者
论文摘要
我们考虑一类在分数演算中出现的广义二项式。在建立了一些一般属性之后，我们重点介绍了一个特定但相关的案例，为此我们提供了几种现成的组合身份，包括Pascal规则的改编版本。然后，我们研究相关的生成功能，为其建立递归，组合和整体配方。由此，我们得出了二项式定理的渐近版本。对某些有限总和的组合和渐近分析完成了论文。
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.
