Turán type inequalities for Krätzel functions

Details Turán type inequalities for Krätzel functions Turán type inequalities for Krätzel functions

2011-01-13

arxiv.org/abs/1101.2523v1

Journal of Mathematical Analysis and Applications 388(2) (2012) 716-724

Mathematics

Classical Analysis and ODEs

9 pages

Scientific paper

10.1016/j.jmaa.2011.09.057

Complete monotonicity, Laguerre and Tur\'an type inequalities are established for the so-called Kr\"atzel function $Z_{\rho}^{\nu},$ defined by $$Z_{\rho}^{\nu}(u)=\int_0^{\infty}t^{\nu-1}e^{-t^{\rho}-\frac{u}{t}}\dt,$$ where $u>0$ and $\rho,\nu\in\mathbb{R}.$ Moreover, we prove the complete monotonicity of a determinant function of which entries involve the Kr\"atzel function.

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