关于Euler数和Bernoulli数的推广

Generalizations on Euler's Numbers and Bernoulli's Numbers

本文利用下标算子ｌ及偏下标算子ｌ（ｉ）对Ｅｕｌｅｒ和Ｂｅｒｎｏｕｌｌｉ数进行了推广，给出了ｎ元Ｅｕｌｅｒ数和ｎ元Ｂｅｒｎｏｌｌｉ数的定义，通过导出ｎ元Ｅｕｌｅｒ数和ｎ元Ｂｅｒｎｏｕｌｌｉ数的母函数，从而得到ｎ元Ｅｕｌｅｒ数和ｎ元Ｂｅｒｎｏｕｌｌｉ数的关系式。

In this paper. Euler's numbers and Bernoulli's numbers have been generalized using the subscript operator 1 and 1(i). We give the definitions of Euler's numbers of n--variables and Bernoulli's numbers of n-variables. The mathematical relationships between Euler's numbers of n-variables and Bernoulli's numbers of n-variables were obtained by introducing their generating functions.