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Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation
http://hdl.handle.net/10083/2403
http://hdl.handle.net/10083/240346ca86d0-96c0-4268-96eb-e8233cd9e39b
名前 / ファイル | ライセンス | アクション |
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KJ00004830817.pdf (673.9 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2008-04-30 | |||||
タイトル | ||||||
タイトル | Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Hosoya, Haruo
× Hosoya, Haruo |
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著者(ヨミ) | ||||||
識別子 | 70915 | |||||
識別子Scheme | WEKO | |||||
姓名 | ホソヤ, ハルオ | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Mathematical structure of the families of solutions of Pell equations x^2-Dy^2=1 (called Pell-1) and x^2-Dy^2=-1 (Llep-1) are studied by using Cayley-Hamilton theorem. Besides discovery of several new recursive relations, it was found that the solutions (x_n, y_n) of Pell-1 are expressed by the Chebyshev polynomials of the first and second kinds, T_n and U_n, in terms of the smallest solutions (x_1, y_1). The solutions (t_n, u_n) of Pellep-1 which are the combination of Pell-1 and Llep-1 are expressed by using the conjugate Chebyshev polynomials. Similar results are obtained for the solutions of Pellep-4 through the modified Chebyshev polynomials and their conjugates. The solutions of Pellep-4 with several D values are found to form various interesting mathematical series of numbers, such as Fibonacci, Lucas, Pell numbers. | |||||
書誌情報 |
お茶の水女子大學自然科學報告 巻 57, 号 2, p. 19-33, 発行日 2007-01 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00298190 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00033958 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
形態 | ||||||
673899 bytes | ||||||
日本十進分類法 | ||||||
主題Scheme | NDC | |||||
主題 | 400 | |||||
出版者 | ||||||
出版者 | お茶の水女子大学 | |||||
資源タイプ | ||||||
内容記述タイプ | Other | |||||
内容記述 | 紀要論文 | |||||
資源タイプ・ローカル | ||||||
紀要論文 | ||||||
資源タイプ・NII | ||||||
Departmental Bulletin Paper | ||||||
資源タイプ・DCMI | ||||||
text | ||||||
資源タイプ・ローカル表示コード | ||||||
03 |