Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i>
We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-form...
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MDPI AG
2018-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/10/12/675 |
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| author | Serkan Araci Waseem Ahmad Khan Kottakkaran Sooppy Nisar |
| author_facet | Serkan Araci Waseem Ahmad Khan Kottakkaran Sooppy Nisar |
| author_sort | Serkan Araci |
| collection | DOAJ |
| description | We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-formula> and investigate certain symmetric identities involving the polynomials, by mainly using the theory of <i>p</i>-adic integral on <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>. The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities. |
| first_indexed | 2024-04-11T18:23:49Z |
| format | Article |
| id | doaj.art-030fe52324b14b7d87bd95d5d332f6c5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T18:23:49Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-030fe52324b14b7d87bd95d5d332f6c52022-12-22T04:09:41ZengMDPI AGSymmetry2073-89942018-11-01101267510.3390/sym10120675sym10120675Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i>Serkan Araci0Waseem Ahmad Khan1Kottakkaran Sooppy Nisar2Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, TurkeyDepartment of Mathematics, Faculty of Science, Integral University, Lucknow-226026, IndiaDepartment of Mathematics, College of Arts and Science-Wadi Aldawaser, Prince Sattam bin Abdulaziz University, 11991 Riyadh Region, Kingdom of Saudi ArabiaWe aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character <inline-formula> <math display="inline"> <semantics> <mi>χ</mi> </semantics> </math> </inline-formula> and investigate certain symmetric identities involving the polynomials, by mainly using the theory of <i>p</i>-adic integral on <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>. The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.https://www.mdpi.com/2073-8994/10/12/675<i>q</i>-Volkenborn integral on ℤ<i><sub>p</sub></i>Bernoulli numbers and polynomialsgeneralized Bernoulli polynomials and numbers of arbitrary complex ordergeneralized Bernoulli polynomials and numbers attached to a Dirichlet character χ |
| spellingShingle | Serkan Araci Waseem Ahmad Khan Kottakkaran Sooppy Nisar Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i> Symmetry <i>q</i>-Volkenborn integral on ℤ<i><sub>p</sub></i> Bernoulli numbers and polynomials generalized Bernoulli polynomials and numbers of arbitrary complex order generalized Bernoulli polynomials and numbers attached to a Dirichlet character χ |
| title | Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i> |
| title_full | Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i> |
| title_fullStr | Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i> |
| title_full_unstemmed | Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i> |
| title_short | Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character <i>χ</i> |
| title_sort | symmetric identities of hermite bernoulli polynomials and hermite bernoulli numbers attached to a dirichlet character i χ i |
| topic | <i>q</i>-Volkenborn integral on ℤ<i><sub>p</sub></i> Bernoulli numbers and polynomials generalized Bernoulli polynomials and numbers of arbitrary complex order generalized Bernoulli polynomials and numbers attached to a Dirichlet character χ |
| url | https://www.mdpi.com/2073-8994/10/12/675 |
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