Results 21 to 30 of about 39,406 (264)

On some series involving harmonic and skew-harmonic numbers

Journal of Classical Analysis, 2023
In this paper, we evaluate in closed form several different series involving the harmonic numbers and skew-harmonic numbers. We consider two classes of series involving these sequences. One class of series involves the product of the $n$th harmonic or skew-harmonic number and a tail.
openaire   +2 more sources

On Spieß’s conjecture on harmonic numbers

Discrete Applied Mathematics, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hai-Tao Jin, Lisa Hui Sun
openaire   +2 more sources

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Mathematical and Computer Modelling, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junesang Choi, H. M. Srivastava 0001
openaire   +1 more source

Harmonic numbers as the summation of integrals

CoRR, 2021
4 pages, 16 ...
openaire   +2 more sources

Some results on q-harmonic number sums

Advances in Difference Equations, 2018
In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form ...
Xin Si
doaj   +1 more source

Series of Convergence Rate −1/4 Containing Harmonic Numbers

Axioms, 2023
Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
doaj   +1 more source

Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making [PDF]

Neutrosophic Sets and Systems
As an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets on subset of real numbers. Harmonic mean is a conservative average, which
İrfan DELİ , Vakkas ULUÇAY
doaj   +1 more source

Two problems of binomial sums involving harmonic numbers

Advances in Difference Equations, 2021
Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric ...
Nadia N. Li, Wenchang Chu
doaj   +1 more source

Note on the Higher-Order Derivatives of the Hyperharmonic Polynomials and the r-Stirling Polynomials of the First Kind

Axioms, 2022
In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
doaj   +1 more source

Approximations of the Harmonic Numbers

Results in Mathematics
Abstract The aim of this paper is to present some approximations on the harmonic numbers. Some associated asymptotic series are constructed.
Chao-Ping Chen, Cristinel Mortici
openaire   +1 more source