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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.
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Infinitary harmonic numbers [PDF]
Bulletin of the Australian Mathematical Society, 1990 The infinitary divisors of a natural number n are the products of its divisors of the , where py is an exact prime-power divisor of n and (where yα = 0 or 1) is the binary representation of y. Infinitary harmonic numbers are those for which the infinitary divisors have integer harmonic mean.
Hagis, Peter jun., Cohen, Graeme L.
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Harmonic series with polylogarithmic functions [PDF]
Vojnotehnički Glasnik, 2022 Introduction/purpose: Some sums of the polylogarithmic function associated with harmonic numbers are established. Methods: The approach is based on using the summation methods.
Vuk Stojiljković +2 more
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Open Mathematics, 2023 Hyperharmonic numbers were introduced by Conway and Guy (The Book of Numbers, Copernicus, New York, 1996), whereas harmonic numbers have been studied since antiquity.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Some identities on generalized harmonic numbers and generalized harmonic functions
Demonstratio Mathematica, 2023 The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms.
Kim Dae San, Kim Hyekyung, Kim Taekyun
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Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion
Mathematics, 2022 Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers.
Kwang-Wu Chen
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Congruences for harmonic sums [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Zhao found a curious congruence modulo p on harmonic sums. Xia and Cai generalized his congruence to a supercongruence modulo p². In this paper, we improve the harmonic sums Hₚ(n)=Σ_{l₁+l₂+...+lₙ=p, l₁,l₂,...,lₙ>0} 1/l₁+l₂+...+lₙ to supercongruences ...
Yining Yang, Peng Yang
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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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On q-generalized hyperharmonic numbers with two parameters [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce q-generalized harmonic numbers with two parameters ω and ξ, H_{μ,λ,q}(ω,ξ) for integers μ, λ such that λ ≥ μ. With the help of these numbers, we define a new family of numbers which is called q-generalized hyperharmonic ...
Neşe Ömür, Sibel Koparal, Ömer Duran
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