含Bernoulli数、Euler数、Genocchi数的多重卷积  

Multiple Convolutions on Bernoulli Numbers, Euler Numbers and Genocchi Numbers

作　　者：陈悦 

机构地区：[1]浙江理工大学理学院,浙江 杭州

出　　处：《理论数学》2024年第2期433-443,共11页Pure Mathematics

摘　　要：利用生成函数及双曲函数导子多项式的性质,建立关于Bernoulli数与Euler数的三个多重卷积的递推关系,这三个多重卷积中有两个是Euler型卷积,一个是Rademacher型卷积。又进一步利用部分分式展开法与生成函数方法建立关于Bernoulli数与Genocchi数的混合多重卷积恒等式。In this paper, by using generating functions and the properties of derivative polynomials of the hyperbolic functions, we establish the recurrences of three multiple convolutions on Bernoulli numbers and Euler numbers, including two Euler-type convolutions and one Rademacher-type convolution. Moreover, using the methods of partial fraction decompositions and generating func-tions, we present a mixed multiple convolution identity on Bernoulli numbers and Genocchi numbers.

关 键 词：BERNOULLI数 EULER数 GENOCCHI数 递推关系 生成函数 

分 类 号：O17[理学—数学]