Annihilation Coefficients, Binomial Expansions and q-Analogs
Annihilation Coefficients, Binomial Expansions and q-Analogs作者机构：Department of MathematicsWest Virginia UniversityMorgantownW.Va.26506U.S.A.
出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)
年 卷 期：2010年第30卷第2期
页 面：191-204页
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
主 题：Annihilation coefficient Binomial expansion stirling number of the first kind stirling number of the second kind vadermonde convolution.
摘 要：Let {An}∞n=0 be an arbitary sequence of natural numbers. We say A（n,k;A） are the Convolution Annihilation Coefficients for {An}n∞=0 if and only if n∑κ=0A（n,k;A）（x-Aκ）n-k=xn. （0.1） Similary, we define B（n,k;A） to be the Dot Product Annihilation Coefficients for {An}n∞=0 if and only if n∑κ=0A（n,k;A）（x-Aκ）n-k=xn. （0.2） The main result of this paper is an explicit formula for B（n,k;A）, which depends on both k and {An}∞n=0. This paper also discusses binomial and q-analogs of Equations （0.1） and （0.2）.
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