阶乘幂的差分算子及其逆  

The Difference Operator of Factorial Power and Its Inverse

作　　者：孙建新[1] 胡金杰[1] 

机构地区：[1]绍兴文理学院数学系，浙江绍兴312000

出　　处：《绍兴文理学院学报（自然科学版）》2005年第7期22-25,共4页Journal of Shaoxing College of Arts and Sciences

摘　　要：与微分算子及其逆算子积分算子作比较，讨论了差分算子及其逆算子(和分)．主要结果为关于乘积的k-阶差分的Leibniz公式(定理6．3)以及乘积的k-阶和分的对偶公式(定理6．4)。显然，差分算子及其逆算子是阶乘幂多项式的方便工具。In comparison with the differential operator and its inverse - integral operator, the difference operator and its inverse (sum operator) are discussed in this paper. The main results are the Leibniz' formula of difference of k - order of product( Th. 6.3 ) and its dual form - the formula of sum of k - order of product ( Th . 6.4) . Clearly, the difference operator or sum operator is the convenient tool for the polynomial of factorial powers.

关 键 词：差分算子 乘幂 逆算子 积分算子 微分算子 对偶公式 多项式 定理 乘积 

分 类 号：O175.7[理学—数学] TN918.2[理学—基础数学]