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Zeta Functions and the Log-behavior of Combinatorial Sequences
log-convexity Riemann zeta function Bernoulli number Bell number Bessel zeta function Narayana number Hö lder's inequality
2014/6/3
In this paper, we use the Riemann zeta function ζ(x) and the Bessel zeta function ζμ(x) to study the log-behavior of combinatorial sequences. We prove that ζ(x) is log-convex for x>1. As a consequence...
Some New Inequalities for the Gamma, Beta and Zeta Functions
Gamma functions Beta functions Zeta functions Mellin transforms
2008/6/26
An inequality involving a positive linear operator acting on the composition of two continuous functions is presented. This inequality leads to new inequalities involving the Beta, Gamma and Zeta func...
