Results 11 to 20 of about 39,406 (264)
Umbral Methods and Harmonic Numbers
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli +3 more
doaj +8 more sources
On the denominators of harmonic numbers. IV [PDF]
Comptes Rendus. Mathématique, 2022 Let $\mathcal{L}$ be the set of all positive integers $n$ such that the denominator of $1+1/2+\cdots +1/n$ is less than the least common multiple of $1, 2, \dots , n$.
Wu, Bing-Ling, Yan, Xiao-Hui
doaj +3 more sources
Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers [PDF]
Abstract and Applied Analysis, 2014 A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of ...
Junesang Choi
doaj +4 more sources
Harmonic numbers, harmonic series and zeta function [PDF]
Moroccan Journal of Pure and Applied Analysis, 2018 This paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias.
Sebbar Ahmed
doaj +2 more sources
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 harmonic and hyperharmonic Fibonacci numbers [PDF]
Advances in Difference Equations, 2015 In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers.
KESİM, SEYHUN +2 more
openaire +4 more sources
Harmonic numbers and finite groups [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2014 Given a finite group G , let {\tau} (G) be the number of normal subgroups of G ...
Baishya, Sekhar Jyoti, Das, Ashish Kumar
openaire +1 more source
Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We offer a number of various finite and infinite sum identities involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers. For example, among many others, we prove Σⁿₖ₌ₒ((-1)ᵏhₖ/4ᵏ)$binom{2k}{k}$Gₙ₋ₖ = ((-1)ⁿ⁻¹/2^²ⁿ⁻¹)
Necdet Batır, Anthony Sofo
doaj +1 more source
Sharp bounds for harmonic numbers [PDF]
Applied Mathematics and Computation, 2011 7 ...
Bai-Ni Guo, Feng Qi 0001
openaire +2 more sources