Turلn type inequalities for Krنtzel functions

Complete monotonicity, Laguerre and Turán type inequalities are established for the so-called Krätzel function Z ρ ν , defined by Z ρ ν ( u ) = ∫ 0 ∞ t ν − 1 e − t ρ − u t d t , where u > 0 and ρ , ν ∈ R . Moreover, we prove the complete monotonicity of a determinant function of which entries involve the Krätzel function.