分母为奇平方因子的二项式系数级数研究

The series of binomial coefficients of denominator containing square factors

根据一个已知级数,利用正弦积分与Clausen函数的结果,和反正弦积分与Clausen函数的结果,结合积分-裂项方法得到分母为平方因子,以及分母为平方因子与1个,2个,3个1次因子乘积的二项式系数级数.最后给出一组二项式系数级数,并且其和式是函数形式.这样就可以根据需要代入具体的x数值,即可得出一些分母含有奇平方因子的二项式系数数值级数恒等式.这种方法是组合分析的一种新手段.

According to a known series,by using the result of sine integral and Clausen function and the result of inverse chord integral and Clausen function,and by using the integral splitting term method,we obtain the square factor of the denominator and the binomial coefficient series of the denominator as the square factor and the product of 1,2 and 31 times factors Finally,a set of binomial coefficient series is given,and its sum is a functional form.In this way,the numeric series identities involving the odd square factor and the binomial coefficient can be obtained by substituting specific values as needed.This method is a new part of combinatorial analysis.