Results 1 to 10 of about 37,714 (264)
Lerch-harmonic numbers related to Lerch transcendent
Mathematical and Computer Modelling of Dynamical Systems, 2023 Harmonic numbers and generalized harmonic numbers have been studied in connection with combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms.
Taekyun Kim +3 more
doaj +1 more source
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
doaj +1 more source
One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms
Mathematics, 2021 The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers.
Seda Yamaç Akbiyik +2 more
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Some Identities with Special Numbers
Cumhuriyet Science Journal, 2022 In this paper, we derive new identities which are related to some special numbers and generalized harmonic numbers H_n (α) by using the argument of the generating function given in [3] and comparing the coefficients of the generating functions.
Sibel Koparal +2 more
doaj +1 more source