发表机构
College of Teacher Education, Quzhou University; School of Mathematics and Statistics, Anhui Normal University; Department of Mathematics, The Bishop’s School（衢州学院教师教育学院; 安徽师范大学数学与统计学院; 圣公会中学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过迭代积分方法引入形式多重对数函数和一般形式荒川-金子zeta值，建立对偶与求和公式，统一推导已知结果，展现统一性。
AI 中文摘要
我们引入形式多重对数函数（FMPF）和一般形式荒川-金子zeta值（GFAKZVs），并利用迭代积分方法（一种源于代数拓扑的有力工具）建立了若干与普通荒川-金子zeta值类似的有用性质。特别地，我们证明了涉及FMPF和GFAKZVs的各种对偶与求和公式。这使我们能够以统一的方式推导出关于荒川-金子zeta值和金子-津村ψ值的若干已知结果，这些结果先前是通过不同方法获得的，从而凸显了迭代积分形式体系的统一力量。
英文摘要
We introduce a formal multiple polylogarithm function (FMPF) and general formal Arakawa-Kaneko zeta values (GFAKZVs), and establish several useful properties analogous to those of the ordinary Arakawa-Kaneko zeta values by employing the method of iterated integrals, a powerful tool originating in algebraic topology. In particular, we prove various duality and sum formulas involving FMPFs and GFAKZVs. This allows us to derive, in a uniform manner, a number of known results concerning Arakawa-Kaneko zeta values and Kaneko-Tsumura $ψ$-values that were previously obtained by different approaches, thereby highlighting the unifying power of the iterated integral formalism.
Comments16 pages
