退化unipoly-Dedekind DC和的互反关系  

The reciprocity relations associated with degenerate unipoly-Dedekind DC sums

作　　者：李红泽 罗玲玲 马元魁 Hongze Li;Lingling Luo;Yuankui Ma

机构地区：[1]上海交通大学数学科学学院,上海200240 [2]西安工业大学基础学院,西安710021

出　　处：《中国科学：数学》2024年第9期1245-1264,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12171311和12271320)资助项目。

摘　　要：借助退化unipoly-Euler函数和第二类退化unipoly-Euler函数,本文首次定义两类退化unipolyDedekind DC(Daehee-Changhee)和.利用unipoly函数的定义、两类退化Stirling数的定义、退化Genocchi多项式和退化Genocchi数等的定义得到退化unipoly-Euler函数、第二类退化unipoly-Euler函数满足的一些组合恒等式和性质,并证明两类退化unipoly-Dedekind DC和满足互反关系.Based on the degenerate unipoly-Euler functions and type 2 degenerate unipoly-Euler functions,we rst introduce the two types of degenerate unipoly-Dedekind type DC(Daehee-Changhee)sums.By using the de nitions of unipoly functions,degenerate Stirling numbers of the rst kind and the second kind,degenerate Genocchi polynomials,and degenerate Genocchi numbers,we obtain several combinatorial identities and proper-ties of the degenerate unipoly-Euler functions and the type 2 degenerate unipoly-Euler functions.The two types of degenerate unipoly-Dedekind type DC sums are shown to satisfy reciprocity relations.

关 键 词：退化unipoly-Euler多项式 退化unipoly-Genocchi多项式 第二类退化unipoly-Euler多项式 第二类退化unipoly-Genocchi多项式 退化unipoly-Dedekind DC和 第二类退化unipoly-Dedekind DC和 

分 类 号：O156.4[理学—数学]