分母含有奇平方因子的二项式系数倒数级数连带3个整数乘积倒数平方和  

A binomial coefficient reciprocal series with an odd square factor in the denominator is associated with the sum of the reciprocal squares of the product of 3 integers

作　　者：及万会 张来萍 JI Wanhui;ZHANG Laiping(Ningxia Vocational and Technical College for Nationalities, Wuzhong 751100, China;Xinhua College of Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏民族职业技术学院,宁夏吴忠751100 [2]宁夏大学新华学院,宁夏银川750021

出　　处：《南阳师范学院学报》2021年第3期15-24,共10页Journal of Nanyang Normal University

摘　　要：根据一个已知级数,利用余割函数积分,用裂项法给出分母含有平方因子的二项式系数倒数级数连带3个整数乘积倒数平方和,并给出分母含有平方因子的二项式系数倒数级数连带3个整数乘积倒数平方和数值恒等式.On the basis of a known series and using the results of cosecant function integrals,several new binomial coefficient inverse series with an odd square factor in the denominator associated with the sum of the reciprocal squares of the product of 3 integers can be structured by integral-splitting items.Besides,a numerical identity of the binomial coefficient reciprocal series with the square factor in the denominator associated with the sum of the reciprocal squares of the product of 3 integers can also be given.

关 键 词：二项式系数 平方因子 3个整数乘积倒数平方和 余割函数积分 裂项 级数 

分 类 号：O151.22[理学—数学]