Results 21 to 30 of about 146,038 (187)
DENOMINATORS OF BERNOULLI POLYNOMIALS [PDF]
Mathematika, 2018 For a positive integer $n$ let $\mathfrak{P}_n=\prod_{s_p(n)\ge p} p,$ where $p$ runs over all primes and $s_p(n)$ is the sum of the base $p$ digits of $n$. For all $n$ we prove that $\mathfrak{P}_n$ is divisible by all "small" primes with at most one exception.
Bordellès, O. +3 more
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Orthogonalizing q −Bernoulli Polynomials
Demonstratio Mathematica, 2023 In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called O B n ( x , q ) from the q −Bernoulli polynomials. We demonstrate the relationship between O B n ( x , q ) polynomials and the little q ...
Naim Tuglu, SEMRA KUŞ
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FAULHABER POLYNOMIALS AND RECIPROCAL BERNOULLI POLYNOMIALS
Rocky Mountain Journal of Mathematics, 2023 36 pages, 9 tables, 1 figure, final revised ...
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A generalization of the Bernoulli polynomials
Journal of Applied Mathematics, 2003 A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the factorization method introduced by Infeld and Hull (1951).
Natalini, Pierpaolo, Bernardini, Angela
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Advances in Difference Equations, 2019 In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 ...
Dae San Kim +3 more
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Degenerate Bell polynomials associated with umbral calculus
Journal of Inequalities and Applications, 2020 Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials.
Taekyun Kim +4 more
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Generalizations of Bernoulli numbers and polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a, b) are generalized to the one Bn(x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a, b), and Bn(
Qiu-Ming Luo +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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q-Bernoulli numbers and q-Bernoulli polynomials revisited [PDF]
Advances in Difference Equations, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim Taekyun, Lee Byungje, Ryoo Cheon
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Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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