On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials
<p/> <p>In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted <inline-formula><graphic file="1687-1847-2010-765259-i2.gif"/></inline-formul...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2010/765259 |
| _version_ | 1818327349323628544 |
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| author | Rim Seog-Hoon Moon Eun-Jung Jin Jeong-Hee Lee Sun-Jung |
| author_facet | Rim Seog-Hoon Moon Eun-Jung Jin Jeong-Hee Lee Sun-Jung |
| author_sort | Rim Seog-Hoon |
| collection | DOAJ |
| description | <p/> <p>In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted <inline-formula><graphic file="1687-1847-2010-765259-i2.gif"/></inline-formula>-Euler numbers and polynomials. The purpose of this paper is to establish various identities concerning higher-order twisted <inline-formula><graphic file="1687-1847-2010-765259-i3.gif"/></inline-formula>-Euler numbers and polynomials by the properties of <inline-formula><graphic file="1687-1847-2010-765259-i4.gif"/></inline-formula>-adic invariant integral on <inline-formula><graphic file="1687-1847-2010-765259-i5.gif"/></inline-formula>. Especially, if <inline-formula><graphic file="1687-1847-2010-765259-i6.gif"/></inline-formula>, we derive the result of Kim et al. (2009).</p> |
| first_indexed | 2024-12-13T12:14:51Z |
| format | Article |
| id | doaj.art-be0850369df6401d88f910c30a328ad7 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T12:14:51Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-be0850369df6401d88f910c30a328ad72022-12-21T23:46:45ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-0120101765259On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and PolynomialsRim Seog-HoonMoon Eun-JungJin Jeong-HeeLee Sun-Jung<p/> <p>In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted <inline-formula><graphic file="1687-1847-2010-765259-i2.gif"/></inline-formula>-Euler numbers and polynomials. The purpose of this paper is to establish various identities concerning higher-order twisted <inline-formula><graphic file="1687-1847-2010-765259-i3.gif"/></inline-formula>-Euler numbers and polynomials by the properties of <inline-formula><graphic file="1687-1847-2010-765259-i4.gif"/></inline-formula>-adic invariant integral on <inline-formula><graphic file="1687-1847-2010-765259-i5.gif"/></inline-formula>. Especially, if <inline-formula><graphic file="1687-1847-2010-765259-i6.gif"/></inline-formula>, we derive the result of Kim et al. (2009).</p>http://www.advancesindifferenceequations.com/content/2010/765259 |
| spellingShingle | Rim Seog-Hoon Moon Eun-Jung Jin Jeong-Hee Lee Sun-Jung On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials Advances in Difference Equations |
| title | On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials |
| title_full | On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials |
| title_fullStr | On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials |
| title_full_unstemmed | On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials |
| title_short | On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials |
| title_sort | on the symmetric properties of higher order twisted inline formula graphic file 1687 1847 2010 765259 i1 gif inline formula euler numbers and polynomials |
| url | http://www.advancesindifferenceequations.com/content/2010/765259 |
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