含Bernoulli数、Euler数、Genocchi数的多重卷积
Multiple Convolutions on Bernoulli Numbers, Euler Numbers and Genocchi Numbers
DOI: 10.12677/PM.2024.142042, PDF,  被引量    国家自然科学基金支持
作者: 陈 悦：浙江理工大学理学院，浙江 杭州
关键词: Bernoulli数；Euler数；Genocchi数；递推关系；生成函数；Bernoulli Numbers； Euler Numbers； Genocchi Numbers； Recurrence Relations； Generating Functions
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。
Abstract: 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.
文章引用：陈悦. 含Bernoulli数、Euler数、Genocchi数的多重卷积[J]. 理论数学, 2024, 14(2): 433-443. https://doi.org/10.12677/PM.2024.142042

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