A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers
Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x). We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x) in complex plane. We...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/158130 |
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| author | J. Y. Kang C. S. Ryoo |
| author_facet | J. Y. Kang C. S. Ryoo |
| author_sort | J. Y. Kang |
| collection | DOAJ |
| description | Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x). We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x) in complex plane. We find out some identities and properties related to polynomials Ũn(x). Finally, we also derive interesting relations between polynomials Ũn(x), Stirling numbers, central factorial numbers, and Euler numbers. |
| format | Article |
| id | doaj-art-24dc27f06f3d4efc8482fabf24ff51f4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-24dc27f06f3d4efc8482fabf24ff51f42025-08-20T03:54:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/158130158130A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler NumbersJ. Y. Kang0C. S. Ryoo1Department of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaDepartment of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaRecently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x). We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x) in complex plane. We find out some identities and properties related to polynomials Ũn(x). Finally, we also derive interesting relations between polynomials Ũn(x), Stirling numbers, central factorial numbers, and Euler numbers.http://dx.doi.org/10.1155/2013/158130 |
| spellingShingle | J. Y. Kang C. S. Ryoo A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers Journal of Applied Mathematics |
| title | A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers |
| title_full | A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers |
| title_fullStr | A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers |
| title_full_unstemmed | A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers |
| title_short | A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers |
| title_sort | research on a certain family of numbers and polynomials related to stirling numbers central factorial numbers and euler numbers |
| url | http://dx.doi.org/10.1155/2013/158130 |
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