相关论文: Limit formulas for ratios of polygamma functions a…

An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).

We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.

We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.

In the present article we describe a class of algebraic curves on which rational functions of two arguments may reach all their possible limiting values. We also solve a similar question for functions that can be represented as a uniform…

We study the integral representation of $\Gamma$-limits of $p$-coercive integral functionals of the calculus of variations in the spirit of \cite{dalmaso-modica86}. We use infima of local Dirichlet problems to characterize the limit…

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…

Several interesting formulas concerning finite Hilbert transform and logarithmic integrals are proved with application in determining equilibrium measures, planar limits of analytic random matrix models with $1-$cut potential and solving…

This paper gives new explicit formulas for sums of powers of integers and their reciprocals.

This paper evaluates some generalised Euler sums involving the digamma function.

We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of…

Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn…

In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.

In this paper, we will prove some sufficient conditions for the solvability of groups.

Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.

Recently, the properties of a binomial sum related to the multi-link inverted pendulum enumeration problem have been studied. In this note, we establish bounds for this binomial sum.

The main object of this paper is to find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria…

We derive an explicit formula for a restricted partition function P_n^m(s) with constraints making use of known expression for a restricted partition function W_m(s) without constraints

In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…

We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.