Related papers: Sums of series involving central binomial coeffici…
We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward…
We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate…
In this paper we demonstrate the importance of a mathematical constant which is the value of several interesting numerical series involving harmonic numbers, zeta values, and logarithms. We also evaluate in closed form a number of numerical…
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
In this paper, we explore a variety of series involving the central binomial coefficients, highlighting their structural properties and connections to other mathematical objects. Specifically, we derive new closed-form representations and…
Binomial coefficients and harmonic numbers are important in many branches of number theory. With the help of the operator method and several summation and transformation formulas for hypergeometric series, we prove eight conjectural series…
In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…
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…
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.
In this paper, we introduce and study new classes of Ap\'ery-type series involving the multiple $t$-harmonic sums by combining the methods of iterated integral and Fourier--Legendre series expansions, where the multiple $t$-harmonic sums…
In this note, we give an exact formula for a general family of rational zeta series involving the coefficient $\zeta(2n)$ in terms of Hurwitz zeta values. This formula generalizes two formulas from a previous paper of the first author. Our…
We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, complementing and generalizing earlier…
In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.
Gencev has recently reported a closed form summation for an infinite series involving the harmonic numbers and the central binomial numbers. This note indicates a possible approach to the proof involving the dilogarithm function.
We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these…
We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently…
We present explicit formulas for the following family of parametric binomial sums involving harmonic numbers for $p=0,1,2$ and $|t|\leq1$. $$ \sum_{k=1}^{\infty}\frac{H_{k-1}t^k}{k^p\binom{n+k}{k}}\quad \mbox{and}\quad…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…