Related papers: Limit formulas for ratios of polygamma functions a…

In the paper the author simply presents the limit formulas for ratios of derivatives of the gamma function and the digamma function at their singularities.

In the paper, some lower bounds for polygamma functions are refined.

We establish optimal results on limits at infinity for functions in fractional Sobolev spaces.

Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.

In this short note, we obtain error estimates for Riemann sums of some singular functions.

In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or $q$-gamma…

Some inequalities for the ratios of generalized digamma functions are presented. The approache makes use of the series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions.

This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…

In this paper, we prove logarithmically complete monotonicity properties of certain ratios of the $k$-gamma function. As a consequence, we deduce some inequalities involving the $k$-gamma and $k$-trigamma functions.

We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.

In this article we derive some polynomial inequalities for Mertens functions.

In this paper, we prove some inequalities for the differences and ratios of the beta function.

In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.

The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.

A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.

A way to derive an explicit formulae in terms of the potentials, if they are finite-gap, for the solutions of spectral problems and corresponding algebraic curves is presented.

The aim of this note is to give some factorization formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing those existing for Hall-Littlewood functions.

We extend the recent Solymosi's sum-product estimate for reals to the complex case.

An algorithm for computing the limit of a quotient of bivariate real analytic functions has been developed by one of the authors in (Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, 50, 2013, 197…

In this paper, the authors establish some inequalities involving the $q$-extension of the classical Gamma function. These inequalities provide bounds for certain ratios of the $q$-extended Gamma function. The procedure makes use of…