高阶Bernoulli多项式和高阶Euler多项式的关系  

THE RELATIONS BETWEEN HIGHER ORDER BERNOULLI POLYNOMIALS AND HIGHER ORDER EULER POLYNOMIALS

作　　者：雒秋明[1] 马韵新[1] 祁锋[2] 

机构地区：[1]焦作大学数学系,河南焦作454003 [2]焦作工学院应用数学与信息科学系,河南焦作454001

出　　处：《数学杂志》2005年第6期631-636,共6页Journal of Mathematics

基　　金：国家自然科学基金(10001016);河南省自然科学基金(00405180)

摘　　要：利用发生函数的方法,讨论了高阶Bernoulli数和高阶Euler数,高阶Bernoulli多项式和高阶Euler多项式之间的关系,得到了经典Bernoulli数和Euler数,经典Bernoulli多项式和Euler多项式之间的新型关系.In this paper, we comprehensively discuss the relationships between the Bernoulli numbers of higher order and Euler numbers of higher order, between the Bernoulli polynomials of higher order and Euler polynomials of higher order, by using the method of generating functions, and we obtain some new results. Furthermore, we obtain several new relationships between the classical Bernoulli numbers and Euler numbers, between the classical Bernoulli polynomials and Euler polynomials.

关 键 词：Bernoulli-Euler数 Bernoulli-Euler多项式 高阶Bernoulli-Euler数 高阶BernoullliEuler多项式 关系 

分 类 号：O174.6[理学—数学]