Linear harmonic Euler sums with odd and even weight
Applicable Nonlinear Analysis, Volume 2, Issue 3, December 2025, Pages: 182–199
ANTHONY SOFO
College of Sport, Health and Engineering, Victoria University, Australia
JUNESANG CHOI
Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea
Abstract
Euler’s groundbreaking work in the 18th century on linear and nonlinear harmonic sums laid a foundation that continues to inspire mathematical research today. Over the years, many important new discoveries have emerged, deepening our understanding of these fascinating structures. In this paper, we explore various representations of linear harmonic Euler sums of both odd and even weights. The findings highlight not only the rich complexity of this field but also the many opportunities that remain, particularly in the study of multiple zeta values and their generalizations. We also present several new examples of Euler sums with even weight, contributing fresh insights to this enduring area of research.
Cite this Article as
Anthony Sofo and Junesang Choi, Linear harmonic Euler sums with odd and even weight, Applicable Nonlinear Analysis, 2(3), 182–199, 2025