<it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited
<p>Abstract</p> <p>This paper performs a further investigation on the <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It i...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://www.advancesindifferenceequations.com/content/2011/1/33 |
| _version_ | 1818443973539135488 |
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| author | Kim Taekyun Lee Byungje Ryoo Cheon |
| author_facet | Kim Taekyun Lee Byungje Ryoo Cheon |
| author_sort | Kim Taekyun |
| collection | DOAJ |
| description | <p>Abstract</p> <p>This paper performs a further investigation on the <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It is point out that the generating function for the <it>q</it>-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math <b>48</b>, 73-86, 1994) (see Equation 9), some new generating functions for the <it>q</it>-Bernoulli numbers and polynomials are shown.</p> <p><b>Mathematics Subject Classification (2000) </b>11B68, 11S40, 11S80</p> |
| first_indexed | 2024-12-14T19:08:33Z |
| format | Article |
| id | doaj.art-0331a9a4ff3c4be88100262fcee67dc4 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T19:08:33Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-0331a9a4ff3c4be88100262fcee67dc42022-12-21T22:50:47ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472011-01-012011133<it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisitedKim TaekyunLee ByungjeRyoo Cheon<p>Abstract</p> <p>This paper performs a further investigation on the <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It is point out that the generating function for the <it>q</it>-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math <b>48</b>, 73-86, 1994) (see Equation 9), some new generating functions for the <it>q</it>-Bernoulli numbers and polynomials are shown.</p> <p><b>Mathematics Subject Classification (2000) </b>11B68, 11S40, 11S80</p>http://www.advancesindifferenceequations.com/content/2011/1/33Bernoulli numbers and polynomials<it>q</it>-Bernoulli numbers and polynomials<it>q</it>-Bernoulli numbers and polynomials |
| spellingShingle | Kim Taekyun Lee Byungje Ryoo Cheon <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited Advances in Difference Equations Bernoulli numbers and polynomials <it>q</it>-Bernoulli numbers and polynomials <it>q</it>-Bernoulli numbers and polynomials |
| title | <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited |
| title_full | <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited |
| title_fullStr | <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited |
| title_full_unstemmed | <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited |
| title_short | <it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited |
| title_sort | it q it bernoulli numbers and it q it bernoulli polynomials revisited |
| topic | Bernoulli numbers and polynomials <it>q</it>-Bernoulli numbers and polynomials <it>q</it>-Bernoulli numbers and polynomials |
| url | http://www.advancesindifferenceequations.com/content/2011/1/33 |
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