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arXiv · 1305.0938

Turán type inequalities for generalized inverse trigonometric functions

Árpád Baricz·Barkat Ali Bhayo·Matti Vuorinen
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Abstract

In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Turán type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Turán type inequality for a series considered by Ramanujan, involving the digamma function.

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Árpád Baricz, Barkat Ali Bhayo, Matti Vuorinen. 2013-10-25. Turán type inequalities for generalized inverse trigonometric functions. https://doi.org/10.2298/fil1502303b

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