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The inverses of tails of the Riemann zeta function [PDF]
Journal of Inequalities and Applications, 2018 We present some bounds of the inverses of tails of the Riemann zeta function on ...
Donggyun Kim, Kyunghwan Song
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Demonstratio Mathematica, 2022 In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals.
Kim Taekyun +3 more
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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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Fully degenerate Bernoulli numbers and polynomials
Demonstratio Mathematica, 2022 The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Kim Taekyun, Kim Dae San, Park Jin-Woo
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Journal of Scientific Perspectives, 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.
Y. Soykan
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Poly-falling factorial sequences and poly-rising factorial sequences
Open Mathematics, 2021 In this paper, we introduce generalizations of rising factorials and falling factorials, respectively, and study their relations with the well-known Stirling numbers, Lah numbers, and so on.
Kim Hye Kyung
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On Quaternion Gaussian Bronze Fibonacci Numbers
Annales Mathematicae Silesianae, 2022 In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
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, 2021 We show that there exist infinitely many hyperharmonic integers, and this refutes a conjecture of Mező. In particular, for r = 64 ·(2α−1)+32, the hyperharmonic number h ) 33 is integer for 153 different values of α (mod 748 440), where the smallest r is ...
D. C. Sertbas
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Study of degenerate derangement polynomials by λ-umbral calculus
Demonstratio Mathematica, 2023 In the 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators.
Yun Sang Jo, Park Jin-Woo
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On r-Jacobsthal and r-Jacobsthal-Lucas Numbers
Annales Mathematicae Silesianae, 2023 Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences ...
Bilgici Göksal, Bród Dorota
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