Results 31 to 40 of about 10,640,447 (355)

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

Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Mathematics, 2019
In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite⁻Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex.
Shilpi Jain, Khaled Mehrez, Dumitru Baleanu, Praveen Agarwal   +3 more
doaj   +1 more source

On the harmonic number expansion by Ramanujan

Journal of Inequalities and Applications, 2013
Let γ=0.577215664… denote the Euler-Mascheroni constant, and let the sequences The main aim of this paper is to find the values r, s, t, a, b, c and d which provide the fastest sequences (un)n≥1 and (vn)n≥1 approximating the Euler-Mascheroni constant.
C. Mortici, Chao-Ping Chen
semanticscholar   +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.
Choi, Junesang, Srivastava, H. M.
openaire   +1 more source

Five classes of binomial/harmonic series of convergence rate $ -1/4 $

AIMS Mathematics
By applying the 'coefficient extraction method' to the symmetric transformation of hypergeometric series due to Chu and Zhang (2014), we examine systematically five classes of infinite series of convergence rate '$ -1/4 $' containing binomial ...
Chunli Li, Wenchang Chu
doaj   +1 more source

Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
We find various series that involve 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 transformation to ...
Segun Olofin Akerele, Olamide Esther Salami   +1 more
doaj   +1 more source

Spectral signature of short attosecond pulse trains

, 2008
We report experimental measurements of high-order harmonic spectra generated in Ar using a carrier-envelope-offset (CEO) stabilized 12 fs, 800nm laser field and a fraction (less than 10%) of its second harmonic.
Dahlström, Marcus,, Eckle, P, Gaarde, M B, Gallmann, L, Guandalini, A, Holler, M, Keller, U, L'Huillier, Anne,, Lund University., Mansten, Erik,, Mauritsson, Johan,, Ruchon, Thierry,, Schapper, F, Tate, J   +13 more
core   +1 more source

Evaluation of Harmonic Number Series Involving the Binomial Coefficient C(3n,n) in the Denominator by Integration

AppliedMath
Two classes of series involving differences of harmonic numbers and the binomial coefficients C(3n,n) are evaluated in closed form. The classes under consideration are ∑k=0∞H3k+1−Hk(3k+1)3kkkmzkand∑k=0∞H2k−Hk(3k+1)3kkkmzk, where z is a complex number and
Kunle Adegoke, Robert Frontczak
doaj   +1 more source

Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]

Notes on Number Theory and Discrete Mathematics
We consider a polylogarithm expression containing complex arguments, namely 𝓟±(n)=ℜ(Liₙ((1±i)/2)). The central notion of the present paper is to evaluate the real parts of 𝓟±(n) for first four orders, specifically n = 1,2,3, and 4, by constructing ...
Narendra Bhandari
doaj   +1 more source