A Note on the (ℎ,𝑞)-Extension of Bernoulli Numbers and Bernoulli Polynomials

A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials

We observe the behavior of roots of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). The main purpose of this paper is also to investi...

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Main Authors: C. S. Ryoo, T. Kim
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2010/807176
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spelling doaj-e6e67d3abbf043b4a95a34ecd406c9e32020-11-24T23:27:08ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/807176807176A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli PolynomialsC. S. Ryoo0T. Kim1Department of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaDivision of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaWe observe the behavior of roots of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). The main purpose of this paper is also to investigate the zeros of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). Furthermore, we give a table for the zeros of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ).http://dx.doi.org/10.1155/2010/807176
collection DOAJ
language English
format Article
sources DOAJ
author C. S. Ryoo
T. Kim
spellingShingle C. S. Ryoo
T. Kim
A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials
Discrete Dynamics in Nature and Society
author_facet C. S. Ryoo
T. Kim
author_sort C. S. Ryoo
title A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials
title_short A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials
title_full A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials
title_fullStr A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials
title_full_unstemmed A Note on the (โ„Ž,๐‘ž)-Extension of Bernoulli Numbers and Bernoulli Polynomials
title_sort note on the (โ„Ž,๐‘ž)-extension of bernoulli numbers and bernoulli polynomials
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2010-01-01
description We observe the behavior of roots of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). The main purpose of this paper is also to investigate the zeros of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ). Furthermore, we give a table for the zeros of the (โ„Ž,๐‘ž)-extension of Bernoulli polynomials ๐ต(โ„Ž)๐‘›,๐‘ž(๐‘ฅ).
url http://dx.doi.org/10.1155/2010/807176
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AT tkim noteonthehqextensionofbernoullinumbersandbernoullipolynomials
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