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arXiv · 1402.3357

Parameter convexity and concavity of generalized trigonometric functions

D. B. Karp·E. G. Prilepkina
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Abstract

We study the convexity properties of the generalized trigonometric functions considered as functions of parameter. We show that $p\to\sin_p(y)$ and $p\to\cos_p(y)$ are log-concave on the appropriate intervals while $p\to\tan_p(y)$ is log-convex. We also prove similar facts about the generalized hyperbolic functions. In particular, our results settle the major part of a conjecture put forward in a recent paper by Baricz, Bhayo and Vuorinen.

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D. B. Karp, E. G. Prilepkina. 2014-02-14. Parameter convexity and concavity of generalized trigonometric functions. https://arxiv.org/abs/1402.3357

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