Results 11 to 20 of about 11,829,477 (307)
Hypergeometric series and harmonic number identities
Advances in Applied Mathematics, 2005 10 ...
CHU, Wenchang, DEDONNO L.
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On the use of windows for harmonic analysis with the discrete Fourier transform
Proceedings of the IEEE, 1978 F. Harris
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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
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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
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The sum of the telescoping series formed by reciprocals of the cubic polynomials with three different negative integer roots [PDF]
Mathematics in Education, Research and Applications, 2020 This paper deals with the sum of a special telescoping series and is a free follow-up to author’s preceding paper. The terms of this series are reciprocals of the cubic polynomial with three different negative integer roots.
Radovan Potůček
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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.
Dattoli G. +3 more
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Anomalies in Universal Intensity Scaling in Ultrarelativistic Laser-Plasma Interactions [PDF]
, 2008 Laser light incident on targets at intensities such that the electron dynamics is ultrarelativistic gives rise to a harmonic power spectrum extending to high orders and characterized by a relatively slow decay with the harmonic number m that follows a ...
Boyd, T. J. M., Ondarza-Rovira, R.
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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 number theory, elementary particle physics, and theoretical physics.
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Odd harmonic numbers exceed 10²⁴ [PDF]
Mathematics of Computation, 2010 A numbern>1n>1is harmonic ifσ(n)∣nτ(n)\sigma (n)\mid n\tau (n), whereτ(n)\tau (n)andσ(n)\sigma (n)are the number of positive divisors ofnnand their sum, respectively. It is known that there are no odd harmonic numbers up to101510^{15}. We show here that, for any odd numbern>106n>10^6,τ(n)≤n1/3\tau (n)\le n^{1/3}.
Cohen, Graeme L., Sorli, Ronald M.
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Families of Integrals of Polylogarithmic Functions
Mathematics, 2019 We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing ...
Anthony Sofo
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