In this paper, the new application of the generalized trigonometric function (GTF) and of the Ateb function in strong nonlinear dynamic systems is considered. It is found that the GTF and the Ateb function represent the closed-form solution of the purely nonlinear one-degree of freedom oscillator with specific initial conditions. Definition of the GTF and Ateb functions is introduced. In spite of the fact that both functions use the incomplete Beta function and its inverse form, the difference exists according to the definition of both of these functions. The correlation between these two types of functions is exposed. Main properties of the Ateb function and of the special GTF function with parameters \(a = \frac{1}{2}\) and \(b = \frac{1}{\alpha +1}\), which are the solution of the pure nonlinear oscillator, are compared and the value of the functions are calculated. Special attention is directed toward the sine GTF and the cosine Ateb function. Advantages and disadvantages of the both type of solutions are discussed.

本文考虑了广义三角函数（GTF）和Ateb函数在强非线性动力学系统中的新应用。发现GTF和Ateb函数代表具有特定初始条件的纯非线性一自由度振荡器的闭合形式解。介绍了GTF和Ateb函数的定义。尽管两个函数都使用不完整的Beta函数及其反形式，但根据这两个函数的定义存在差异。这两种功能之间的相关性已公开。Ateb函数和带有参数\（a = \ frac {1} {2} \）和\（b = \ frac {1} {\ alpha +1} \）的特殊GTF函数的主要属性比较纯非线性振荡器的解，并计算函数值。特别注意正弦GTF和余弦Ateb函数。讨论了两种解决方案的优缺点。