Related papers: On Some Summation Formulas
By combining the telescoping method with an algebraic relation, four classes of binomial moments are examined. Several explicit summation formulae are established.
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.
Given a suitable arithmetic function h, we investigate the average order of h as it ranges over the values taken by an integral binary form F. A general upper bound is obtained for this quantity, in which the dependence upon the…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
In this paper we establish a new summation method by expanding $\prod_{k}(1-\frac{z}{a_{k}})^{-1}$ with two approaches: the Taylor expansion and the infinite partial fraction decomposition. Here we focus on the case when $a_{k}$ is…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…
We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…
An interplay between the sum of certain series related to Harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
From the solution of the heat and mass diffusion equations that describe the exothermic physical absorption of a gas into a liquid, compact formulae for the sums of two infinite series are derived. The method is general and should be…
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…
Various product and sum relationships are established using special functions, specifically involving Special functions. These relationships are derived from formulas inspired by the finite sum that incorporates the Hurwitz-Lerch zeta…
We prove several supercongruences involving the harmonic number of order two $H_n^{(2)}:=\sum_{k=1}^n1/k^2$. For example, if $p>5$ is prime and $\alpha$ is $p$-integral, then we can completely determine $$…
In this note, we present a simple summation formula for $k$-bonacci numbers. The derivation consists in obtaining the generating function of such numbers, and noting that its evaluation at a particular value yields a formula generalizing a…
The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to…
In this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators. We show that several previous results on different contexts (absolutely summing, almost summing, Cohen summing) are particular cases…
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term…