基于Zeta函数的Mellin变换及其应用  

Mellin transformation and its application on Zeta function

作　　者：郝梦 王昱丹 HAO Meng;WANG Yudan(School of Science,Tianjin University of Technology and Education,Tianjin 300222,China)

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《高师理科学刊》2024年第5期13-16,共4页Journal of Science of Teachers＇College and University

摘　　要：Mellin变换是一种以幂函数为积分核的积分变换,常用于广义留数定理、信号处理和渐进展开理论的相关研究中.从Mellin变换理论出发,基于Mellin变换与Fourier变换、Zeta函数的相互关系,推导了Zeta函数与Gamma函数相乘的Mellin变换形式,结合Euler乘积公式详细讨论了Mellin变换在Zeta函数变换中的应用方法和技巧.Mellin transformation is a kind of integral transformation with power function as integral kernel,which is often used in the research of generalized residue theorem,signal processing and progressive expansion theory.Based on Mellin transformation theory and the relationship between Mellin transformation,Fourier transformation and Zeta function,the transformation form of Mellin transformation in the multiplication of Zeta function and Gamma function is derived.The application method and technique of Mellin transformation in Zeta function transformation are discussed in detail with Euler product formula.

关 键 词：Mellin变换 FOURIER变换 ZETA函数 Hurwitz Zeta函数 

分 类 号：O177.65[理学—数学]