Results 21 to 30 of about 101,104 (278)
Generalized hypergeometric Bernoulli numbers [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales.
Kalyan Chakraborty, Takao Komatsu
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Fast Calculation of Bernoulli Numbers
Современные информационные технологии и IT-образование, 2019 Bernoulli numbers are often found in mathematical analysis, number theory, combinatorics, and other areas of mathematics. In some monographs on number theory there are separate chapters devoted only to Bernoulli numbers and their properties.
Rustem R. Aidagulov, Sergei T. Glavatsky
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Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
Mathematics, 2016 In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli ...
Feng Qi, Bai-Ni Guo
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Bernoulli Related Polynomials and Numbers [PDF]
Mathematics of Computation, 1979 The polynomials φ n ( x ; a , b ) {\varphi _n}(x;a,b) of degree n defined by the equations \[ Δ a φ n ( x
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BERNOULLI'S LAW OF LARGE NUMBERS [PDF]
ASTIN Bulletin, 2013 AbstractThis year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science.
Bolthausen, Erwin, Wüthrich, Mario V
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Advances in Difference Equations, 2010 We define the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomials attached to χ of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain
L.-C. Jang +5 more
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Combinatorics of poly-Bernoulli numbers
, 2015 The ${\mathbb B}_n^{(k)}$ poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers ($B_n={\mathbb B}_n^{(1)}$) --- were introduced by Kaneko in 1997. When the parameter $k$ is negative then ${\mathbb B}_n^{(k)}$ is a nonnegative
Bényi, Beáta, Hajnal, Peter
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q-Bernoulli Numbers Associated with q-Stirling Numbers
Advances in Difference Equations, 2008 We consider Carlitz q-Bernoulli numbers and q-Stirling numbers of the first and the second kinds. From the properties of q-Stirling numbers, we derive many interesting formulas associated with Carlitz q-Bernoulli numbers. Finally, we will prove βn,q=â
Taekyun Kim
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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