Results 31 to 40 of about 109 (99)
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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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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On some conjectures on the monotonicity of some arithmetical sequences [PDF]
, 2012 2010 Mathematics Subject Classification: Primary 11B65, 11B68, 05A10; Secondary 11B83.Here, we prove some conjectures on the monotony of combinatorial and number– theoretical sequences from a recent paper of Zhi–Wei ...
Luca, Florian, Stănică, Pantelimon
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A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
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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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The log-convexity of the poly-Cauchy numbers
, 2017 In 2013, Komatsu introduced the poly-Cauchy numbers, which generalizeCauchy numbers. Several generalizations of poly-Cauchy numbers have been con-sidered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In
Komatsu, Takao +3 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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Differential equations associated with generalized Bell polynomials and their zeros
Open Mathematics, 2016 In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials.
Ryoo Seoung Cheon
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Fully degenerate Bell polynomials associated with degenerate Poisson random variables
Open Mathematics, 2021 Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al.
Kim Hye Kyung
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Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants [PDF]
, 2012 MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the ...
Savic, Natasa +2 more
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