分母为平方因子的二项式系数倒数级数

The Series of Reciprocal of Binomial Coefficients of Denominator Containing Square Factors

根据一个已知级数,利用反正弦积分与多对数的结果,用积分-裂项法给出分母为1个平方因子,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.利用反三角函数与反双曲函数关系给出分母为平方因子的交错二项式系数倒数级数.所给出二项式系数倒数级数的和式是函数形式.并给出分母含有平方因子的二项式系数倒数数值级数恒等式.

Using one known series,using integral of Arcsin and polylogarithm,we can structure several new series of reciprocal of binominal coefficients by integral-splitting items.Their denominator factor has a square,and square factor and 1,2,3 product of each factor.Using relation of inverse Trigonometric and Hyperbolic function we get that alternating series of reciprocal of binominal coefficients of denominator Containing square factors.And some series of reciprocal of numbers values of binominal coefficients of denominator containing square factors are given.The method of split items offered in this paper is a new combinatorial analysis way and a elementary method to construct new series.