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In this article, using Stirling’s formula, the series-expansion of digamma functions and other techniques, some inequalities and monotonicity concerning the ratio of gamma functions are obtained,… (More)
In this paper, by using Fourier series theory, several summing formulae for Riemann Zeta function ζ(s) and Dirichlet series are deduced.
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
In the paper, the authors verify that the geometric mean of many positive numbers is a complete Bernstein function of degree $$0$$0 and, consequently, a positive operator monotone function.
In the paper, the authors present some properties, including convexity, complete monotonicity, product inequalities, and determinantal inequalities, of the large Schröder numbers and find three… (More)
In the paper, by virtue of the Fa\`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first… (More)
In the paper, the authors present monotonicity results of a function involving the inverse hyperbolic sine. From these, the authors derive some inequalities for bounding the inverse hyperbolic… (More)
In the paper, by virtue of the Faa di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the… (More)
In the paper, by methods of the theory of majorization, the authors establish the Schur m-convexity and Shannon type inequalities for Kapur’s entropy.
In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative… (More)