Results 41 to 50 of about 10,388 (168)
Some new identities on the twisted carlitz's
Journal of Inequalities and Applications, 2011 In this paper, we consider the twisted Carlitz's q-Bernoulli numbers using p-adic q-integral on ℤ p . From the construction of the twisted Carlitz's q-Bernoulli numbers, we investigate some properties for the twisted Carlitz's q-Bernoulli numbers ...
Kim Taekyun +3 more
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International Journal of Mathematics and Mathematical Sciences, 2004 We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)=∑n=1∞(qn(s−1)/[n]s ...
Taekyun Kim
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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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Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials
Advances in Difference Equations, 2020 The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper,
Taekyun Kim +3 more
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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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On the 𝑞-Bernoulli Numbers and Polynomials with Weight 𝜶
Abstract and Applied Analysis, 2011 We present a systemic study of some families of higher-order 𝑞-Bernoulli numbers and polynomials with weight 𝛼. From these studies, we derive some interesting identities on the 𝑞-Bernoulli numbers and polynomials with weight 𝛼.
T. Kim, J. Choi
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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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Cubic harmonics and Bernoulli numbers
Journal of Combinatorial Theory, Series A, 2012 18 pages, 3 ...
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Известия Иркутского государственного университета: Серия "Математика", 2016 The Bernoulli polynomials for natural x were first considered by J.Berno\-ulli (1713) in connection with the problem of summation of the powers of consecutive positive integers. For arbitrary $x$ these polynomials were studied by L.Euler.
O. Shishkina
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Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods
Axioms, 2018 In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol ...
Yilmaz Simsek
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