Tur\'an type inequalities for Kr\"atzel functions
  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. 
\'Arp\'ad Baricz, Dragana Jankov, Tibor K. Pog\'any
math.CA