Results 11 to 20 of about 1,693 (108)
CYCLOTOMIC POLYNOMIALS WITH PRESCRIBED HEIGHT AND PRIME NUMBER THEORY
Mathematika, Volume 67, Issue 1, Page 214-234, January 2021., 2021 Abstract Given any positive integer n, let A(n) denote the height of the nth cyclotomic polynomial, that is its maximum coefficient in absolute value. It is well known that A(n) is unbounded. We conjecture that every natural number can arise as value of A(n) and prove this assuming that for every pair of consecutive primes p and p′ with p⩾127, we have ...
Alexandre Kosyak +3 more
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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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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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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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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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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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On the denominators of harmonic numbers [PDF]
, 2017 Let $H_n$ be the $n$-th harmonic number and let $v_n$ be its denominator. It is well known that $v_n$ is even for every integer $n\ge 2$. In this paper, we study the properties of $v_n$.
Chen, Yong-Gao, Wu, Bing-Ling
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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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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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