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Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.", "subitem_description_type": "Abstract"}]}, "item_6_description_30": {"attribute_name": "資源タイプ（コンテンツの種類）", "attribute_value_mlt": [{"subitem_description": "Article", "subitem_description_type": "Other"}]}, "item_6_description_5": {"attribute_name": "引用", "attribute_value_mlt": [{"subitem_description": "JOURNAL OF MATHEMATICAL PHYSICS. 55(1):013502 (2014)", "subitem_description_type": "Other"}]}, "item_6_link_3": {"attribute_name": "信州大学研究者総覧へのリンク", "attribute_value_mlt": [{"subitem_link_text": "Odake, Satoru", "subitem_link_url": "http://soar-rd.shinshu-u.ac.jp/profile/ja.uhLeuUkV.html"}]}, "item_6_link_67": {"attribute_name": "WoS", "attribute_value_mlt": [{"subitem_link_text": "Web of Science", "subitem_link_url": "http://gateway.isiknowledge.com/gateway/Gateway.cgi?\u0026GWVersion=2\u0026SrcAuth=ShinshuUniv\u0026SrcApp=ShinshuUniv\u0026DestLinkType=FullRecord\u0026DestApp=WOS\u0026KeyUT=000330907400028"}]}, "item_6_publisher_4": {"attribute_name": "出版者", "attribute_value_mlt": [{"subitem_publisher": "AMER INST PHYSICS"}]}, "item_6_relation_48": {"attribute_name": "DOI", "attribute_value_mlt": [{"subitem_relation_name": [{"subitem_relation_name_text": "10.1063/1.4859795"}], "subitem_relation_type_id": {"subitem_relation_type_id_text": "https://doi.org/10.1063/1.4859795", "subitem_relation_type_select": "DOI"}}]}, "item_6_rights_62": {"attribute_name": "権利", "attribute_value_mlt": [{"subitem_rights": "Copyright© 2014 AIP Publishing LLC."}]}, "item_6_select_64": {"attribute_name": "著者版フラグ", "attribute_value_mlt": [{"subitem_select_item": "author"}]}, "item_6_source_id_35": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0022-2488", "subitem_source_identifier_type": "ISSN"}]}, "item_6_source_id_39": {"attribute_name": "NII ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0022-2488", "subitem_source_identifier_type": "ISSN"}]}, "item_6_source_id_40": {"attribute_name": "書誌レコードID", "attribute_value_mlt": [{"subitem_source_identifier": "AA00701758", "subitem_source_identifier_type": "NCID"}]}, "item_6_text_70": {"attribute_name": "wosonly keywords", "attribute_value_mlt": [{"subitem_text_value": "DISCRETE QUANTUM-MECHANICS; X-L LAGUERRE; CRUMS THEOREM; POTENTIALS; SYSTEMS"}]}, "item_6_textarea_68": {"attribute_name": "wosonly abstract", "attribute_value_mlt": [{"subitem_textarea_value": "Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters. © 2014 AIP Publishing LLC."}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Odake,  Satoru"}], "nameIdentifiers": [{"nameIdentifier": "35914", "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": "2015-09-28"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "Equivalences_multi-indexed_orthogonal_polynomials.pdf", "filesize": [{"value": "257.1 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_note", "mimetype": "application/pdf", "size": 257100.00000000003, "url": {"label": "Equivalences_multi-indexed_orthogonal_polynomials.pdf", "url": "https://soar-ir.repo.nii.ac.jp/record/11715/files/Equivalences_multi-indexed_orthogonal_polynomials.pdf"}, "version_id": "ed2304b7-82af-401e-9427-d030d1fb35b1"}]}, "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": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Equivalences of the multi-indexed orthogonal polynomials", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "Equivalences of the multi-indexed orthogonal polynomials", "subitem_title_language": "en"}]}, "item_type_id": "6", "owner": "1", "path": ["1170"], "permalink_uri": "http://hdl.handle.net/10091/17869", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2014-09-05"}, "publish_date": "2014-09-05", "publish_status": "0", "recid": "11715", "relation": {}, "relation_version_is_last": true, "title": ["Equivalences of the multi-indexed orthogonal polynomials"], "weko_shared_id": -1}