Results 11 to 20 of about 1,005 (113)
Learning linear non-Gaussian graphical models with multidirected edges
Journal of Causal Inference, 2021 In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data.
Liu Yiheng, Robeva Elina, Wang Huanqing
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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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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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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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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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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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Harmonic number identities via polynomials with r-Lah coefficients
, 2020 In this paper, polynomials whose coefficients involve r -Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
L. Kargin, M. Can
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Sparse binary cyclotomic polynomials [PDF]
, 2011 We derive a lower and an upper bound for the number of binary cyclotomic polynomials $\Phi_m$ with at most $m^{1/2+\epsilon}$ nonzero terms.Comment: 3 ...
Bzdega, Bartlomiej
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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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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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