基于一个抽球模型的组合恒等式及组合解释(英文)

COMBINATORIAL IDENTITY AND COMBINATORIAL EXPLANATION BASED ON A DRAWING BALL MODEL

本文研究了抽球概率模型的问题.利用概率方法,获得了关于第一类Stirling数和广义可重复二项式系数的无限求和形式的组合恒等式以及有关组合解释,推广了Stirling数和二项式系数的无限求和结果.

Two cases that s black or white balls will be placed back with drawn ball are studied. By probabilistic method, combinatorial identities or combinatorial explanations related to the Stirling number of the first kind and generalized binomial coefficient with repetition are given by considering the probability of drawing k white balls in n trials and the probability of that n trials are required until the kth white ball is drawn. Some infinite summations on the Stirling number and binomial coefficients are generalized.