Results 11 to 20 of about 47,314 (210)
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, Olivier +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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IET Networks, EarlyView., 2022 Abstract Everything can be connected in the Internet of Things (IoTs) technology that enables efficient communication between connected objects. IoTs industry‐based meta‐heuristic and mining algorithms, which are considered an important field of Artificial Intelligence will be used to construct a healthcare application in this study for lowering costs,
Muhaned Al‐Hashimi +4 more
wiley +1 more source
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 ton.
Dae San Kim, Taekyun Kim 0001
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Intent Arabic text categorisation based on different machine learning and term frequency
IET Networks, EarlyView., 2022 Abstract The complexity of Internet network configurations has made managing networks a complicated undertaking. Intent‐Based Networking (IBN) is a potential solution to this issue. In contrast to conventional networks, where a concrete description of the settings typically conveys a network administrator's goal kept on each device, an administrator's ...
Mohammad Fadhil Mahdi +1 more
wiley +1 more source
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−Legendre polynomials, and derive a generalized formula for O B n ( x , q ) by leveraging the ...
Naim Tuglu, SEMRA KUŞ
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Illustrating Implications of Misaligned Causal Questions and Statistics in Settings With Competing Events and Interest in Treatment Mechanisms. [PDF]
Stat MedABSTRACT In the presence of competing events, many investigators are interested in a direct treatment effect on the event of interest that does not capture treatment effects on competing events. Classical survival analysis methods that treat competing events like censoring events, at best, target a controlled direct effect: the effect of the treatment ...
Kawahara T, McGrath S, Young JG.
europepmc +2 more sources
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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Series of sums of products of higher-order Bernoulli functions
Journal of Inequalities and Applications, 2017 It is shown in a previous work that Faber-Pandharipande-Zagier’s and Miki’s identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions.
Taekyun Kim +3 more
doaj +1 more source
Journal of Applied Mathematics, 2021 Asymptotic approximations of Tangent polynomials, Tangent-Bernoulli, and Tangent-Genocchi polynomials are derived using saddle point method and the approximations are expressed in terms of hyperbolic functions.
Cristina B. Corcino +2 more
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