含二项式系数与排列数的交错级数型线性微分方程

Solution of the Interlace Series Type Linear Differential Equation Containing Binomial Coefficient and Arrangement Number

通过把系数含有二项式系数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程,找出了求这类方程通解的方法与理论,把所得定理给出了严格的证明,并通过实例介绍了它的应用.

By transforming the interlace series type linear differential equation with coefficient containing binomial coefficients and arrangement number into the linear differential equation of successive integral, the theory and method for solving this kind of equation are determined. The theorem obtained is proved strictly and the application is introduced through examples.