In this paper we study the inverse of the eigenfunction sinpof 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.
- Bernstein functions
- Completely monotone functions
- Eigenfunctions of p-Laplacian
- Generalized trigonometric function
- Turán-type inequalities
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