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Inequalities for Cyclic Functions
Authors:Horst Alzer  Stephan Ruscheweyh  Luis Salinas
Institution:Morsbacher Strasse 10, 51545, Waldbröl, Germanyf1;Mathematisches Institut, Universität Würzburg, 97074, Würzburg, Germany, f2;Departamento de Informática, Universidad Técnica F. Santa María, Valparaíso, Chile, f3
Abstract:The nth cyclic function is defined by

We prove that if k is an integer with 1kn−1, then

holds for all positive real numbers x with the best possible constantsα=1 and β= 2n-k over n.
Keywords:inequalities  cyclic functions  gamma function
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