基于超几何级数的中心二项式系数恒等式  

Central Binomial Coefficient Identities Based on Hypergeometric Series

作　　者：刘红梅 金萱 李若慧 LIU Hong-mei;JIN Xuan;LI Ruo-hui(School of Science, Dalian Minzu University, Dalian Liaoning 116650, China)

机构地区：[1]大连民族大学理学院,辽宁大连116650

出　　处：《大连民族大学学报》2022年第1期35-37,共3页Journal of Dalian Minzu University

摘　　要：为建立新的中心二项式系数恒等式,本文基于两个超几何级数求和公式,利用微分的方法,结合Gamma函数和Digamma函数的性质,推导出两个新的含有中心二项式系数和调和数的无穷限级数求和公式。两个级数恒等式的获得是超几何级数理论应用于组合恒等式的进一步体现。To establish new identities for central binomial coefficients,two new infinite summation formulas involving central binomial coefficients and harmonic numbers are obtained by the differential method and some properties of Gamma function and Digamma function in this paper,which is based on hypergeometric series summation formulas.The acquisition of the two series identities is a further embodiment of the application of hypergeometric series theory to combinatorial identities.

关 键 词：超几何级数 中心二项式系数 调和数 

分 类 号：O174.6[理学—数学]