Results 11 to 20 of about 111 (99)
A STUDY ON THE SUMS OF SQUARES OF GENERALIZED TRIBONACCI NUMBERS: CLOSED FORM FORMULAS OF ∑_{k=0}ⁿkx^{k}W_{k}² [PDF]
, 2021 In this paper, closed forms of the sum formulas ∑_{k=0}ⁿkx^{k}W_{k}², ∑_{k=0}ⁿkx^{k}W_{k+2}W_{k} and ∑_{k=0ⁿkx^{k}W_{k+1}W_{k} for the squares of generalized Tribonacci numbers are presented.
Yüksel SOYKAN, SOYKAN, Yüksel
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Study on r-truncated degenerate Stirling numbers of the second kind
Open Mathematics, 2022 The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some ...
Kim Taekyun, Kim Dae San, Kim Hyekyung
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On hyperbolic k-Pell quaternions sequences [PDF]
, 2018 In this paper we introduce the hyperbolic k-Pell functions and new classes of quaternions associated with this type of functions are presented.
Catarino, Paula
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A note on polyexponential and unipoly Bernoulli polynomials of the second kind
Open Mathematics, 2021 In this paper, the authors study the poly-Bernoulli numbers of the second kind, which are defined by using polyexponential functions introduced by Kims. Also by using unipoly function, we study the unipoly Bernoulli numbers of the second kind, which are ...
Ma Minyoung, Lim Dongkyu
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On the type 2 poly-Bernoulli polynomials associated with umbral calculus
Open Mathematics, 2021 Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques.
Kim Taekyun +3 more
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Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers
Open Mathematics, 2021 In this paper, with the aid of the Faà di Bruno formula and by virtue of properties of the Bell polynomials of the second kind, the authors define a kind of notion of degenerate Narumi numbers and polynomials, establish explicit formulas for degenerate ...
Qi Feng +2 more
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The GCD Sequences of the Altered Lucas Sequences
Annales Mathematicae Silesianae, 2020 In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
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A Further Generalization of limn→∞n!/nn=1/e{\lim _{n \to \infty }}\root n \of {n!/n} = 1/e
Annales Mathematicae Silesianae, 2022 It is well-known, as follows from the Stirling’s approximation n!∼2πn(n/e)nn! \sim \sqrt {2\pi n{{\left( {n/e} \right)}^n}}, that n!/n→1/en\root n \of {n!/n \to 1/e}.
Farhadian Reza, Jakimczuk Rafael
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Demonstratio Mathematica, 2022 In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
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About the existence of the thermodynamic limit for some deterministic sequences of the unit circle
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 12, Page 857-863, 2000., 2000 We show that in the set Ω=ℝ+×(1,+∞)⊂ℝ+2, endowed with the usual Lebesgue measure, for almost all (h, λ) ∈ Ω the limit limn→+∞(1/n)ln|h(λn−λ−n)mod[-12,12)| exists and is equal to zero. The result is related to a characterization of relaxation to equilibrium in mixing automorphisms of the two‐torus.
Stefano Siboni
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