Results 1 to 10 of about 11,317,597 (199)
New Harmonic Number Series [PDF]
AppliedMathBased on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived.
Kunle Adegoke, Robert Frontczak
doaj +4 more sources
Harmonic number identities via polynomials with r-Lah coefficients
Comptes Rendus. Mathématique, 2020 In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
Kargın, Levent, Can, Mümün
doaj +2 more sources
On the Ramanujan-Lodge harmonic number expansion
Applied Mathematics and Computation, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
C. Mortici, M. Villarino
semanticscholar +4 more sources
On the denominators of harmonic numbers, III [PDF]
Periodica Mathematica Hungarica, 2022 Let ℒ be the set of all positive integers n such that the denominator of 1
Wu, Bing-Ling, Yan, Xiao-Hui
openaire +3 more sources
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
Unitary Harmonic Numbers [PDF]
Proceedings of the American Mathematical Society, 1975 If d ∗
Hagis, Peter jun., Lord, Graham
openaire +1 more source
Polynomials related to harmonic numbers and evaluation of harmonic number series II [PDF]
Applicable Analysis and Discrete Mathematics, 2011 In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers. 2000 Mathematics Subject Classification. 11B73, 11B75, 11B83.
Ayhan Dil, Veli Kurt
openaire +5 more sources
On the use of windows for harmonic analysis with the discrete Fourier transform
Proceedings of the IEEE, 1978 F J Harris
exaly +2 more sources
A note on harmonic number identities, Stirling series and multiple zeta values [PDF]
International Journal of Number Theory, 2018 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, studied before amongst others by Candelpergher and Coppo ...
Markus Kuba, A. Panholzer
semanticscholar +1 more source
Generalization in diffusion models arises from geometry-adaptive harmonic representation [PDF]
International Conference on Learning Representations, 2023 Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but recent reports of
Zahra Kadkhodaie +3 more
semanticscholar +1 more source