Results 31 to 40 of about 120 (102)
Polynomials related to harmonic numbers and evaluation of harmonic number series II
, 2010 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 ...
Veli Kurt, Ayhan Dil
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A Hybrid Matrix–Based Encoding Scheme With Error Detection via Third‐Order Recurrences
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we propose a novel encoding–decoding algorithm based on third‐order linear recurrence sequences and their associated matrix representations. In particular, third‐order Jacobsthal and third‐order Jacobsthal–Lucas matrix sequences are combined with Padovan and Perrin matrix sequences to construct a hybrid block–based coding scheme.
Sukran Uygun, Smritijit Sen
wiley +1 more source
Annales Mathematicae Silesianae, 2020 Let {rn}n∈ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e.
Farhadian Reza, Jakimczuk Rafael
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Normal ordering associated with λ-Stirling numbers in λ-shift algebra
Demonstratio Mathematica, 2023 It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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On the ψ− Sheffer F− Polynomials and Their Degenerate Matrices
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we systematically construct a novel framework within umbral calculus by integrating the structures of generalized F‐calculus and degenerate sequences. Utilizing Roman’s foundational approach to umbral calculus, we first introduce a new family of ψ − F− linear functionals and their corresponding ψ − F− differential operators on the ...
Semra Kuş, Smritijit Sen
wiley +1 more source
Generalized apostol-type polynomial matrix and its algebraic properties [PDF]
, 2019 The aim of this paper is to introduce the generalized Apostol-type polynomial matrix W [m−1,α](x;c,a;λ;µ;ν) and the generalized Apos-tol-type matrix W [m−1,α](c,a;λ;µ;ν).
Ramírez, William +2 more
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A new member of the Pell sequences: The pseudo-Pell sequence [PDF]
In this study, we define a new family of the Pell numbers and establish some properties of the relation to the ordinary Pell numbers. We give some identities the pseudo-Pell numbers.
GÖKBAŞ, Hasan
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Narayana Numbers With Zeckendorf Partition in Two Terms
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The Narayan’s cow sequence starts with the terms 1, 1, and 1. Each subsequent term is obtained as the sum of the previous term and the term three places before. A term of this sequence is called a Narayana number. The mathematician Zeckendorf proved that every positive integer has a unique decomposition into a sum of distinct and nonconsecutive ...
Japhet Odjoumani +2 more
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Zeros distribution and interlacing property for certain polynomial sequences
Open MathematicsIn this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
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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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