Results 41 to 50 of about 1,563 (216)
Congruences for Bernoulli numbers and Bernoulli polynomials
Discrete Mathematics, 1997 The Bernoulli numbers and polynomials are defined by \(B_0=1\), \(\sum^{n-1}_{k=0}{n\choose k} B_k= 0\) \((n=2,3,\dots)\) and \(B_n(x)= \sum^n_{k=0}{n\choose k} B_{n-k} x^k\), respectively. Two basic congruences for Bernoulli numbers are the Kummer congruences (used in the theory of Fermat's last theorem) and the von Staudt-Clausen theorem. There exist
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q-Bernoulli numbers and polynomials
Duke Mathematical Journal, 1948 Verf. definiert die \(q\)-Bernoullischen Zahlen \(\beta_m\) durch \(\beta_0=1\), \(\beta_1=-1/(q+1)\) und die symboli\-sche Rekursionsformel \(q(q\beta+1)^m=0\) \((m>1)\), wobei \(\beta^i\) nach Entwicklung durch \(\beta_i\) zu ersetzen ist. Die Zahlen \(\beta_m\) stimmen für \(q=1\) mit den gewöhnlichen Bernoullischen Zahlen überein.
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A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials [PDF]
Transactions of the American Mathematical Society, 1996 Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta functions for totally real numbers. The coefficients of such polynomials are finite combinations of products of Bernoulli numbers which are difficult to get hold of.
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Arithmetical properties of double Möbius-Bernoulli numbers
Open Mathematics, 2019 Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x).
Bayad Abdelmejid, Kim Daeyeoul, Li Yan
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Applied Economic Perspectives and Policy, EarlyView.ABSTRACT This paper examines the relationship between participation in the EU Rural Development Program and the economic performance of Italian olive farms using a finite‐mixture model with inverse‐probability‐weighted regression adjustment. Based on 2010–2022 FADN panel data, it estimates heterogeneous treatment effects while correcting for selection ...
Francesco Caracciolo, Marilena Furno
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A Note on the Modified q-Bernoulli Numbers and Polynomials with Weight α
Abstract and Applied Analysis, 2011 A systemic study of some families of the modified q-Bernoulli numbers and polynomials with weight α is presented by using the p-adic q-integration ℤp.
T. Kim +4 more
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On p-Bernoulli numbers and polynomials
Journal of Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Physics‐Grounded Probabilistic Bits for Hardware‐Efficient Intelligent Inference and Optimization
Advanced Intelligent Systems, EarlyView.Si–SiNx interface traps are harnessed as a complementary metal–oxide–semiconductor‐compatible source of controllable randomness for probabilistic bits. Pulse‐width‐programmed stochastic capture converts nanoscale defect dynamics into Boltzmann‐consistent binary outputs, while a physics‐based Simulation Program with Integrated Circuit Emphasis model ...
Dokyoung Lee +3 more
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On hypergeometric Bernoulli numbers and polynomials [PDF]
Acta Mathematica Hungarica, 2017 In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
Hu, S., Kim, M.-S.
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Deep Underground Science and Engineering, EarlyView.This study proposes an eco‐friendly coal permeability enhancement technique by utilizing mine waste gangue as an abrasive in high‐pressure water jets. Integrating erosion experiments with smoothed particle hydrodynamics‐finite element method coupled simulations, the research study elucidates the flow field dynamics and a nonlinear solid–liquid ...
Qingxiang Wang +4 more
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