Results 51 to 60 of about 109 (99)
Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences
Open MathematicsThe Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }.
Qi Jinyun, Guo Victor Zhenyu
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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
core
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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A new formula for the coefficients of Gaussian polynomials
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of ...
Andrica Dorin, Bagdasar Ovidiu
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A new family of q-Bernstein polynomials: probabilistic viewpoint
Arab Journal of Basic and Applied SciencesIn this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming [Formula: see text] is a random variable satisfying moment conditions, we use the generating function of ...
Ayse Karagenc +2 more
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Probabilistic degenerate Bernstein polynomials
Applied Mathematics in Science and EngineeringIn recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier.
Jinyu Wang +3 more
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On a generalization of derangement polynomials and numbers
Demonstratio MathematicaIn T. Kim, D. S. Kim, and D. V. Dolgy, Probabilistic derangement numbers and polynomials, Math. Comput. Model. Dyn. Syst. 31 (2025), no. 1, 2529188, Kim-Kim defined the probabilistic derangement polynomials and numbers and found some properties of those ...
Yun Sang Jo, Park Jin-Woo
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On a family of q-modified-Laguerre-Appell polynomials
Arab Journal of Basic and Applied SciencesThis paper aims to introduce a new class of special polynomials called q-modified Laguerre-Appell polynomials. Some definitions and concepts related to this class of polynomials, including generating function and series definition are explored.
Mohammed Fadel, Abdulghani Muhyi
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