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INEQUALITIES AND TURÁNIANS FOR SOME SPECIAL FUNCTIONS

A. LAFORGIA

Department of Mathematics, Roma Tre University, Largo San Leonardo Murialdo, 1 00146, Rome, Italy

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P. NATALINI

Department of Mathematics, Roma Tre University, Largo San Leonardo Murialdo, 1 00146, Rome, Italy

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https://doi.org/10.1142/9789812770752_0036Cited by:2 (Source: Crossref)

Abstract:

We use a generalization of the Schwarz inequality to prove Turán-type inequalities for some special functions, such as the polygamma and the Riemann ζ functions. Finally we extend to x > 0 the range of validity of a lower bound for the function , proved by Elbert and Laforgia only for , p > 1. This function is related to gamma and incomplete gamma functions by .