Euler Basis, Identities, and Their Applications
Let Vn={p(x)∈ℚ[x]|deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. We show that {E0(x),E1(x),…,En(x)} is a good basis for the space Vn, for our purpose of arithmetical and combinatorial applications. Thus, if p(x)∈ℚ[x] is of degree n, then p(x)=∑l=0nblEl(x) for some uniquely determined bl∈...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/343981 |
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| _version_ | 1841524652906643456 |
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| author | D. S. Kim T. Kim |
| author_facet | D. S. Kim T. Kim |
| author_sort | D. S. Kim |
| collection | DOAJ |
| description | Let Vn={p(x)∈ℚ[x]|deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. We show that {E0(x),E1(x),…,En(x)} is a good basis for the space Vn, for our purpose of arithmetical and combinatorial applications. Thus, if p(x)∈ℚ[x] is of degree n, then p(x)=∑l=0nblEl(x) for some uniquely determined bl∈ℚ. In this paper we develop method for computing bl from the information of p(x). |
| format | Article |
| id | doaj-art-a6612dcecd034d4ca5b2817e0b3055ea |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a6612dcecd034d4ca5b2817e0b3055ea2025-02-03T05:47:41ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/343981343981Euler Basis, Identities, and Their ApplicationsD. S. Kim0T. Kim1Department of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaLet Vn={p(x)∈ℚ[x]|deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. We show that {E0(x),E1(x),…,En(x)} is a good basis for the space Vn, for our purpose of arithmetical and combinatorial applications. Thus, if p(x)∈ℚ[x] is of degree n, then p(x)=∑l=0nblEl(x) for some uniquely determined bl∈ℚ. In this paper we develop method for computing bl from the information of p(x).http://dx.doi.org/10.1155/2012/343981 |
| spellingShingle | D. S. Kim T. Kim Euler Basis, Identities, and Their Applications International Journal of Mathematics and Mathematical Sciences |
| title | Euler Basis, Identities, and Their Applications |
| title_full | Euler Basis, Identities, and Their Applications |
| title_fullStr | Euler Basis, Identities, and Their Applications |
| title_full_unstemmed | Euler Basis, Identities, and Their Applications |
| title_short | Euler Basis, Identities, and Their Applications |
| title_sort | euler basis identities and their applications |
| url | http://dx.doi.org/10.1155/2012/343981 |
| work_keys_str_mv | AT dskim eulerbasisidentitiesandtheirapplications AT tkim eulerbasisidentitiesandtheirapplications |