Related papers: About Factorial Sums

An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.

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 present a new variant of the Faa di Bruno formula with a simpler summation order.

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.

In this paper we provide a family of inequalities, extending a recent result due to Albuquerque et al.

In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

A survey of mean inequalities with real weights is given.

An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…

We provide a new characterization of the logarithmic Sobolev inequality.

In the present work we give several new integral inequalities of the type Riemann-Liouville fractional integral via Montgomery identities integrals.

In this paper we discuss and prove some new strong convergence theorems for partial sums and Fej\'er means with respect to the Vilenkin system.

Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The…

We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).

Powers of Fibonacci polynomials are expressed as single sums, improving on a double sum recently seen in the literature.

The aim of the present paper is to obtain some new fractional integral inequalities for convex functions. Saigo fractional integral operator is used to establish the results.

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…

We prove the irrationality of some factorial series. To do so we combine methods from elementary and analytic number theory with methods from the theory of uniform distribution.