arXiv:2610.33121v1 Announce Type: new Abstract: In this work we present an extension of the classical trigonometric functions which include, amongst others, the Lindqvist p-trigonometric functions. Additionally, we show their relevance in the study of certain versions of the nonlinear harmonic oscillator equation. Furthermore, we study their more important mathematical properties and obtain their corresponding Pythagorean-like relations. We also define a new extension of the Beta and Ateb sine functions using these new $\chi$-trigonometric functions. Indeed, these new Beta and Ateb functions are involved in the closed form expressions obtained for the solutions of the nonlinear oscillator under certain constraints.
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