{"created":"2021-03-01T06:39:55.323573+00:00","id":34622,"links":{},"metadata":{"_buckets":{"deposit":"e9d92997-05a7-47a6-81af-dc914090486e"},"_deposit":{"id":"34622","owners":[],"pid":{"revision_id":0,"type":"depid","value":"34622"},"status":"published"},"_oai":{"id":"oai:teapot.lib.ocha.ac.jp:00034622","sets":["347:359:684"]},"item_11_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2007-01","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"33","bibliographicPageStart":"19","bibliographicVolumeNumber":"57","bibliographic_titles":[{"bibliographic_title":"お茶の水女子大學自然科學報告"}]}]},"item_11_description_17":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_11_description_46":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"紀要論文","subitem_description_type":"Other"}]},"item_11_description_7":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Other"}]},"item_11_full_name_2":{"attribute_name":"著者(ヨミ)","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"70915","nameIdentifierScheme":"WEKO"}],"names":[{"name":"ホソヤ, ハルオ"}]}]},"item_11_publisher_36":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"お茶の水女子大学"}]},"item_11_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN00033958","subitem_source_identifier_type":"NCID"}]},"item_11_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"00298190","subitem_source_identifier_type":"ISSN"}]},"item_11_subject_20":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"400","subitem_subject_scheme":"NDC"}]},"item_11_text_18":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_text_value":"673899 bytes"}]},"item_11_text_47":{"attribute_name":"資源タイプ・ローカル","attribute_value_mlt":[{"subitem_text_value":"紀要論文"}]},"item_11_text_48":{"attribute_name":"資源タイプ・NII","attribute_value_mlt":[{"subitem_text_value":"Departmental Bulletin Paper"}]},"item_11_text_49":{"attribute_name":"資源タイプ・DCMI","attribute_value_mlt":[{"subitem_text_value":"text"}]},"item_11_text_50":{"attribute_name":"資源タイプ・ローカル表示コード","attribute_value_mlt":[{"subitem_text_value":"03"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Hosoya, Haruo"}],"nameIdentifiers":[{"nameIdentifier":"70914","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-04-19"}],"displaytype":"detail","filename":"KJ00004830817.pdf","filesize":[{"value":"673.9 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KJ00004830817.pdf","url":"https://teapot.lib.ocha.ac.jp/record/34622/files/KJ00004830817.pdf"},"version_id":"aa5d472a-f343-492d-ad49-435d2947032d"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation"}]},"item_type_id":"11","owner":"1","path":["684"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-04-30"},"publish_date":"2008-04-30","publish_status":"0","recid":"34622","relation_version_is_last":true,"title":["Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-12T05:39:00.693092+00:00"}