Results 1 to 10 of about 1,084 (165)
Bernoulli F-polynomials and Fibo–Bernoulli matrices [PDF]
Advances in Difference Equations, 2019 In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
Mathematics, 2023 In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and ...
Dionisio Peralta +2 more
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Bernoulli Basis and the Product of Several Bernoulli Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We develop methods for computing the product of several Bernoulli and Euler polynomials by using Bernoulli basis for the vector space of polynomials of degree less than or equal to n.
Dae San Kim, Taekyun Kim
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A note on the Bernoulli and Euler polynomials
Applied Mathematics Letters, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gi-Sang Cheon
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An identity of symmetry for the Bernoulli polynomials
Discrete Mathematics, 2008 The author proves an identity of symmetry for the higher Bernoulli polynomials. It turns out implies that the recurrence relation and multiplication theorem for the Bernoulli polynomials discussed by \textit{F. T. Howard} [J. Number Theory 52, No. 1, 157--172 (1995; Zbl 0844.11019)], as well as a relation of symmetry between the power sum polynomials ...
Sheng-Liang Yang
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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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Values of Bernoulli polynomials [PDF]
Pacific Journal of Mathematics, 1996 The main objective of this paper is to derive a formula for the expression \(B_{p-1} (a/q)- B_{p- 1}\bmod p\). Here, \(p\) is an odd prime, \(q\) and \(a\) are relatively prime integers, \(1\leq a\leq q\), and \(p\) does not divide \(q\). \(B_n\) means the Bernoulli number and \(B_n (t)\) the \(n\)th Bernoulli polynomial.
Granville, Andrew, Sun, Zhi-Wei
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Representations of degenerate poly-Bernoulli polynomials
Journal of Inequalities and Applications, 2021 As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions of such functions and polynomials, degenerate polylogarithm functions were introduced and degenerate poly-Bernoulli polynomials
Taekyun Kim +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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Computation, 2020 In this work, we derive the operational matrix using poly-Bernoulli polynomials. These polynomials generalize the Bernoulli polynomials using a generating function involving a polylogarithm function.
Chang Phang +2 more
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