Results 11 to 20 of about 37,250 (282)
Umbral Methods and Harmonic Numbers [PDF]
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
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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
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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
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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
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Iterated harmonic numbers [PDF]
, 2023 13 pages, 2 ...
J Marshall Ash +3 more
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Identities between harmonic, hyperharmonic and Daehee numbers [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we present some identities relating the hyperharmonic, the Daehee and the derangement numbers, and we derive some nonlinear differential equations from the generating function of a hyperharmonic number.
Seog-Hoon Rim, Taekyun Kim, Sung-Soo Pyo
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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
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On Harmonic Complex Balancing Numbers
Mathematics, 2022 In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini ...
Fatih Yılmaz +2 more
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Evaluating Infinite Series Involving Harmonic Numbers by Integration [PDF]
MathematicsEight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series W is introduced
Chunli Li, Wenchang Chu
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Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order
MathematicsWe study the formulas for binomial sums of harmonic numbers of higher order ∑k=0nHk(r)nk(1−q)kqn−k=Hn(r)−∑j=1nDr(n,j)qjj. Recently, Mneimneh proved that D1(n,j)=1. In this paper, we find several different expressions of Dr(n,j) for r≥1.
Takao Komatsu, B. Sury
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