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Abstract：
This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications.
摘要：
本研究深入研究了一类特殊的广义p-三角函数，检查它们与已建立的对应函数的连接，如p余弦和p正弦函数。我们在这里探索称为p-versine的新类函数，p-coversine,p-haversine,和p-hacovercosine，通过提供全面的定义和属性。基于p余弦和p正弦函数的特性，新提出的函数提供了独特的数学见解。我们的工作有助于全面了解这些新的特殊功能，展示它们在不同科学领域的潜在应用，从数学分析到物理和工程。本文作为未来应用数学研究人员的宝贵资源，参与这些新的数学函数，增强从不同的实际应用中建模复杂模式的能力。
