关于分母为奇平方因子的二项式系数倒数级数  

Series of Reciprocal of Binomial Coefficents of Denominator Containing Odd Square Factors

作　　者：张来萍[1] 唐永鲁 及万会[1] ZHANG Lai-ping;TANG Yong-lu;JI Wan-hui(Yinchan Energy College,Yinchuan,Ningxia 750105,China)

机构地区：[1]银川能源学院基础部,宁夏银川750105

出　　处：《河北北方学院学报（自然科学版）》2018年第3期1-10,共10页Journal of Hebei North University:Natural Science Edition

基　　金：宁夏自然科学基金项目(NZ12208);银川能源学院科研项目(2015-KY-Y-49)

摘　　要：目的根据一个已知级数,给出分母为平方因子,平方因子与1个、2个、3个奇因子乘积的二项式系数倒数级数。方法利用正弦积分与Clausen函数,用积分-裂项法给出分母为平方因子,平方因子与1个、2个、3个奇因子乘积的二项式系数倒数级数。结果给出分母含有平方因子的二项式系数倒数数值恒等式。结论所给出二项式系数级数的和式是函数形式。Objective According to a known series,the reciprocal series of binomial coefficients is given in which the denominator is the square factor,and the square factor is the product of1,2and3odd factors.Methods By using integral of sin and Clausen function,several new series of reciprocal of binominal coefficients are structured by splitting items.Their denominator factor has a square factor and and square factor is the product of1,2and3odd factors.Results The numerical identities of the binomial coefficients with the square factor in the denominator are given.Conclusion The sum of the series of binomial coefficients has a function form.

关 键 词：二项式系数 平方因子 Clausen函数 倒数 积分裂项 级数 

分 类 号：O174.5[理学—数学]