发表机构
University of Akdeniz（安塔利亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造 Apostol-Dedekind 和的指数生成函数，定义高阶和及相关有限和族，并利用这些函数推导出许多新公式。
AI 中文摘要
本文的主要目标之一是构造 Apostol-Dedekind 和的生成函数。这些指数生成函数极大地促进了涉及这些和的新公式和关系的发现。本文的其他主要目标是定义高阶 Apostol-Dedekind 和以及某些其他有限和族，并构造它们的生成函数。这些生成函数包括 Bernoulli 多项式和数、Euler 多项式和数、Array 多项式、Stirling 数、Carlitz 多项式及其偏导数方程，以及 Hardy 和等。此外，通过使用这些函数，推导出了许多关于高阶 Apostol-Dedekind 和的新公式。
英文摘要
One of the primary objectives of this paper is to construct generating functions for Apostol-Dedekind sums. These exponential generating functions greatly facilitate the discovery of new formulas and relations involving these sums. Other primary objectives of this paper are to define Apostol-Dedekind sums of higher-order and other certain family of finite sums, and to construct their generating functions. These generating functions include the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the Array polynomials, the Stirling numbers, the Carlitz polynomials with their partial derivative equations, and the Hardy sums etc. Moreover, by using these functions, many novel formulas for the Apostol-Dedekind sums of higher-order are derived.
