Neuman, Edward Inequalities involving a logarithmically convex function and their applications to special functions. (English) Zbl 1132.26337 JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 16, 4 p. (2006). Summary: It has been shown that if \( f\) is a differentiable, logarithmically convex function on nonnegative semi-axis, then the function \( [f(x)]^a/f(ax)\), (\( a \geq 1\)) is decreasing on its domain. Applications to inequalities involving gamma function, Riemann’s zeta function, and the complete elliptic integrals of the first kind are included. Cited in 1 ReviewCited in 5 Documents MSC: 26D07 Inequalities involving other types of functions 26D20 Other analytical inequalities 33B15 Gamma, beta and polygamma functions 11M06 \(\zeta (s)\) and \(L(s, \chi)\) Keywords:logarithmically convex functions; inequalities; gamma function; Riemann’s zeta function; complete elliptic integrals of the first kind PDF BibTeX XML Cite \textit{E. Neuman}, JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 16, 4 p. (2006; Zbl 1132.26337) Full Text: EuDML EMIS OpenURL