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arXiv · 1903.07407

Applications of generalized trigonometric functions with two parameters

Hiroyuki Kobayashi·Shingo Takeuchi
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Abstract

Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of works on GTFs concerning the $p$-Laplacian. However, few applications to differential equations unrelated to the $p$-Laplacian are known. We will apply GTFs with two parameters to nonlinear nonlocal boundary value problems without $p$-Laplacian. Moreover, we will give integral formulas for the functions, e.g. Wallis-type formulas, and apply the formulas to the lemniscate function and the lemniscate constant.

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Hiroyuki Kobayashi, Shingo Takeuchi. 2019-03-19. Applications of generalized trigonometric functions with two parameters. https://doi.org/10.3934/cpaa.2019072

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