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Generalized trigonometric functions and elementary applications. (English) Zbl 1397.33001

Summary: We present some applications of the generalized trigonometric functions to problems in classical mechanics and to the theory of integral equations. We discuss how second and third order trigonometries are ideally suited tools to treat either damped harmonic oscillators and three dimensional rotational models. We make further progress in the generalization process by discussing the properties of Laguerre trigonometries along with the relevant link with the theory of Bessel functions.

MSC:

33B10 Exponential and trigonometric functions
44A05 General integral transforms
45J05 Integro-ordinary differential equations
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