Results 51 to 60 of about 120 (102)
Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
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Demonstratio MathematicaThe study of special functions has become an enthralling area in mathematics because of its properties and wide range of applications that are relevant into other fields of knowledge.
Corcino Cristina B. +2 more
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Bidimensional Extensions of Cobalancing and Lucas-Cobalancing Numbers
Annales Mathematicae SilesianaeA new bidimensional version of cobalancing numbers and Lucas-balancing numbers are introduced. Some properties and identities satisfied by these new bidimensional sequences are studied.
Chimpanzo J. +4 more
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Fourier series of functions involving higher-order ordered Bell polynomials
Open Mathematics, 2017 In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the ...
Kim Taekyun +3 more
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Generalized Chebyshev Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2018 Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
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A New Statistic for the 3x + 1 Problem
, 2007 A nite (3x + 1){trajectory is a sequence a = a1 ; : : : ; an of positive integers such that a i+1 = 3a i + 1 if a i is odd, a i+1 = a i =2 if a i is even, a i > 1 if i < n and an = 1.
David Gluck, Brian D. Taylor
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Recurrence for probabilistic extension of Dowling polynomials
Open MathematicsSpivey found a remarkable recurrence relation for Bell numbers, which was generalized to that for Bell polynomials by Gould-Quaintance. The aim of this article is to generalize their recurrence relation for Bell polynomials to that for the probabilistic ...
Ma Yuankui +3 more
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A study on a type of degenerate poly-Dedekind sums
Demonstratio MathematicaDedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations. As a new generalization of the Dedekind sums, the degenerate poly-Dedekind sums, which are obtained from the Dedekind sums by replacing ...
Ma Yuankui +4 more
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In Search of the Truly Marvelous Proof
: Fermat's Last Theorem (FLT), proposed in 1637 by Pierre de Fermat, states that no positive integers a,b, and c satisfy the equation a^n+b^n=c^n for any integer n>2.
Charles Kusniec
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Proving Fermat’s Last Theorem Using Partial Differences of Powers and the Binomial Theorem
: Fermat's Last Theorem (FLT), proposed in 1637 by Pierre de Fermat, states that no positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer n > 2.
Charles Kusniec
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