{"created":"2023-06-20T16:47:55.518482+00:00","id":19702,"links":{},"metadata":{"_buckets":{"deposit":"8a1652f1-806c-44bf-9336-7a314b6f84c8"},"_deposit":{"created_by":3,"id":"19702","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"19702"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00019702","sets":["14:2667:4459"]},"author_link":["33445","33448","33452","33451","33446","33447","33453","33449","33450"],"item_8_biblio_info_21":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2018","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"5","bibliographicPageStart":"1","bibliographic_titles":[{"bibliographic_title":"科学研究費助成事業研究成果報告書 (2017)"}]}]},"item_8_description_33":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"研究成果の概要（和文）：超幾何微分方程式に含まれる3つの固有パラメータに大きなパラメータを1次関数として導入するとＷＫＢ解と呼ばれる形式解が構成できる。この構成は代数的、初等的に可能であるが得られた解は一般に発散し、そのままでは解析的な意味を持たない。この形式的に解をボレル総和法を適用することができ、解析的な解が構成できる。一方、超幾何微分方程式には超幾何関数で表示される標準的な解析解が知られている。本研究では、これらの古典的な解とＷＫＢ解のボレル和として得られる解の間の線型関係式を明らかにした。応用として超幾何関数のパラメータに関する漸近展開の公式を一般に得た。ストークス現象を記述する式も併せて得られている。\n研究成果の概要（英文）：Introducing a large parameter in the 3 parameters contained in the Gauss hypergeometric differential equation, we can construct the WKB solutions which are formal solutions to the equation. The construction is done algebraically and elementarily, however, these formal solutions are divergent in general and do not have analytic sense. We may apply the Borel resummation method to the formal solutions and can construct analytic solutions and bases of the solution space. On the other hand, the Gauss hypergeometric differential equation has standard bases of solutions expressed by the hypergeometric function. In this research, we have obtained linear relations between these two classes of bases. As an application, asymptotic expansion formulas with respect to the large parameter of the Gauss hypergeometric function have been obtained. At the same time, we have some formulas which describe the parametric Stokes phenomena of the WKB solutions.","subitem_description_type":"Abstract"}]},"item_8_description_36":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究種目：基盤研究(C);  研究期間：2014～2017;   課題番号：26400126;   研究分野：代数解析学;   科研費の分科・細目：","subitem_description_type":"Other"}]},"item_8_description_37":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"Research Paper","subitem_description_type":"Other"}]},"item_8_description_41":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_8_publisher_14":{"attribute_name":"出版者 名前","attribute_value_mlt":[{"subitem_publisher":"近畿大学"}]},"item_8_relation_11":{"attribute_name":"著者 外部リンク","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-26400126/"}]}]},"item_8_text_10":{"attribute_name":"著者 役割","attribute_value_mlt":[{"subitem_text_value":"研究代表者/研究分担者/研究分担者/連携研究者/連携研究者/連携研究者/連携研究者/連携研究者/連携研究者"}]},"item_8_text_7":{"attribute_name":"著者(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"AOKI,Takashi"},{"subitem_text_language":"en","subitem_text_value":"SUZUKI,Takao"},{"subitem_text_language":"en","subitem_text_value":"NAKAMURA,Yayoi"},{"subitem_text_language":"en","subitem_text_value":"HONDA,Naofumi"},{"subitem_text_language":"en","subitem_text_value":"KAWAI,Takahiro"},{"subitem_text_language":"en","subitem_text_value":"TAKEI,Yoshitsugu"},{"subitem_text_language":"en","subitem_text_value":"YAMAZAKI,Susumu"},{"subitem_text_language":"en","subitem_text_value":"KOIKE,Tatsuya"},{"subitem_text_language":"en","subitem_text_value":"UMETA,Yoko"}]},"item_8_text_8":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"近畿大学理工学部; 教授"},{"subitem_text_value":"近畿大学理工学部; 准教授"},{"subitem_text_value":"近畿大学理工学部; 准教授"},{"subitem_text_value":"北海道大学大学院理学系研究員; 准教授"},{"subitem_text_value":"京都大学数理解析研究所; 名誉教授"},{"subitem_text_value":"京都大学数理解析研究所; 准教授"},{"subitem_text_value":"日本大学理工学部; 教授"},{"subitem_text_value":"神戸大学大学院理学研究科; 准教授"},{"subitem_text_value":"城西大学理学部; 准教授"}]},"item_8_text_9":{"attribute_name":"著者所属(翻訳)","attribute_value_mlt":[{"subitem_text_value":"Kindai University"},{"subitem_text_value":"Kindai University"},{"subitem_text_value":"Kindai University"}]},"item_8_version_type_12":{"attribute_name":"版","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_be7fb7dd8ff6fe43","subitem_version_type":"NA"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"青木, 貴史"},{"creatorName":"アオキ, タカシ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"鈴木, 貴雄"},{"creatorName":"スズキ, タカオ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"中村, 弥生"},{"creatorName":"ナカムラ, ヤヨイ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"本多, 尚文"},{"creatorName":"ホンダ, ナオフミ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"河合, 隆裕"},{"creatorName":"カワイ, タカヒロ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"竹井, 義次"},{"creatorName":"タケイ, ヨシツグ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"山崎, 晋"},{"creatorName":"ヤマサキ, ススム","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"小池, 達也"},{"creatorName":"コイケ, タツヤ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"梅田, 陽子"},{"creatorName":"ウメタ, ヨウコ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-11-20"}],"displaytype":"detail","filename":"26400126seika.pdf","filesize":[{"value":"2.6 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"26400126seika.pdf","url":"https://kindai.repo.nii.ac.jp/record/19702/files/26400126seika.pdf"},"version_id":"c9c3de23-840c-437d-9deb-459375707c4d"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"超幾何微分方程式","subitem_subject_scheme":"Other"},{"subitem_subject":"超幾何関数","subitem_subject_scheme":"Other"},{"subitem_subject":"ＷＫＢ解","subitem_subject_scheme":"Other"},{"subitem_subject":"特異摂動","subitem_subject_scheme":"Other"},{"subitem_subject":"ストークス現象","subitem_subject_scheme":"Other"},{"subitem_subject":"漸近展開","subitem_subject_scheme":"Other"},{"subitem_subject":"ボレル総和法","subitem_subject_scheme":"Other"},{"subitem_subject":"合流型超幾何微分方程式","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"パラメトリック・ストークス現象の代数解析","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"パラメトリック・ストークス現象の代数解析"},{"subitem_title":"Algebraic analysis of parametric Stokes phenomena","subitem_title_language":"en"}]},"item_type_id":"8","owner":"3","path":["4459"],"pubdate":{"attribute_name":"公開日","attribute_value":"2018-11-20"},"publish_date":"2018-11-20","publish_status":"0","recid":"19702","relation_version_is_last":true,"title":["パラメトリック・ストークス現象の代数解析"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-06-20T21:34:01.276042+00:00"}