数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2011年
4期
665-669
,共5页
概率模型%组合恒等式%Stirling数%非中心Stirling数
概率模型%組閤恆等式%Stirling數%非中心Stirling數
개솔모형%조합항등식%Stirling수%비중심Stirling수
probabilistic model%combinatorial identity%Stirling number%noncentral Stirling number
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.
本文研究瞭抽毬概率模型的問題.利用概率方法,穫得瞭關于第一類Stirling數和廣義可重複二項式繫數的無限求和形式的組閤恆等式以及有關組閤解釋,推廣瞭Stirling數和二項式繫數的無限求和結果.
본문연구료추구개솔모형적문제.이용개솔방법,획득료관우제일류Stirling수화엄의가중복이항식계수적무한구화형식적조합항등식이급유관조합해석,추엄료Stirling수화이항식계수적무한구화결과.
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.
