Parameter convexity and concavity of generalized trigonometric functions

We study the convexity properties of the generalized trigonometric functions viewed as functions of the parameter. We show that p→sinp⁡(y) and p→cosp⁡(y) are log-concave on the appropriate intervals while p→tanp⁡(y) is log-convex. We also prove similar facts about the generalized hyperbolic function...

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Vydané v:	Journal of mathematical analysis and applications Ročník 421; číslo 1; s. 370 - 382
Hlavní autori:	Karp, D.B., Prilepkina, E.G.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.01.2015
Predmet:	Eigenfunctions of p-Laplacian Generalized hyperbolic functions Generalized trigonometric functions Log-concavity Log-convexity Turán type inequality Log-concavity Generalized trigonometric functions Generalized hyperbolic functions Eigenfunctions of p-Laplacian Turán type inequality Log-convexity
ISSN:	0022-247X, 1096-0813
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