Related papers: About Factorial Sums

In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…

In this paper we prove and discuss some new $\left( H_p,L_{p}\right)$ type inequalities for partial Sums and Fej\'er means with respect to Walsh system. It is also proved that these results are the best possible in a special sense. As…

In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument. We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler…

New cases of the multiplicity conjecture are considered.

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

Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.

Equivalencies of many basic elementary inequalities are given

Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…

We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…

We give solutions of a Diophantine equation containing factorials, which can be written as a cubic form, or as a sum of binomial coefficients. We also give some solutions to higher degree forms and relate some solutions to an unsolvable…

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.

In the paper, the authors establish some interesting identities and inequalities involving the extended Weyl type fractional integrals.

An approach to constructing an upper bound for the Riemann-Farey sum is described.

We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…

We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference…

Let $A$ be a subset of $\mathbb{Z} / N\mathbb{Z}$ and let $\mathcal{R}$ be the set of large Fourier coefficients of $A$. Properties of $\mathcal{R}$ have been studied in works of M.-- C. Chang, B. Green and the author. In the paper we…

We improve an existing result on exponential quadrilinear sums in the case of sums over multiplicative subgroups of a finite field and use it to give a new bound on exponential sums with quadrinomials.

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.