{"id":"https://openalex.org/W2016162097","doi":"https://doi.org/10.48550/arxiv.0801.4137","title":"Continuous biorthogonality of the elliptic hypergeometric function","display_name":"Continuous biorthogonality of the elliptic hypergeometric function","publication_year":2008,"publication_date":"2008-01-27","ids":{"openalex":"https://openalex.org/W2016162097","doi":"https://doi.org/10.48550/arxiv.0801.4137","mag":"2016162097"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:0801.4137","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0801.4137","pdf_url":"https://arxiv.org/pdf/0801.4137","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0801.4137","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078547197","display_name":"Vyacheslav Pavlovich Spiridonov","orcid":"https://orcid.org/0000-0002-6091-4512","observed_orcids":["https://orcid.org/0000-0002-6091-4512"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Spiridonov, V. P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5078547197"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.6279000043869019,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.6279000043869019,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.15780000388622284,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.12349999696016312,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/elliptic-hypergeometric-functions","display_name":"elliptic hypergeometric functions","score":0.953000009059906},{"id":"https://openalex.org/keywords/sklyanin-algebras","display_name":"Sklyanin algebras","score":0.9850000143051147},{"id":"https://openalex.org/keywords/elliptic-hypergeometric-series","display_name":"elliptic hypergeometric series","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C92941272","wikidata":"https://www.wikidata.org/wiki/Q1062958","display_name":"Basic hypergeometric series","level":3,"score":0.7617303133010864},{"id":"https://openalex.org/C181881257","wikidata":"https://www.wikidata.org/wiki/Q4780998","display_name":"Appell series","level":5,"score":0.7189937829971313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.611194372177124},{"id":"https://openalex.org/C148160416","wikidata":"https://www.wikidata.org/wiki/Q783948","display_name":"Confluent hypergeometric function","level":3,"score":0.6070195436477661},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.5763440728187561},{"id":"https://openalex.org/C158241908","wikidata":"https://www.wikidata.org/wiki/Q109744257","display_name":"Generalized hypergeometric function","level":3,"score":0.567783772945404},{"id":"https://openalex.org/C123958593","wikidata":"https://www.wikidata.org/wiki/Q938102","display_name":"Elliptic function","level":2,"score":0.5334107279777527},{"id":"https://openalex.org/C122343491","wikidata":"https://www.wikidata.org/wiki/Q3754612","display_name":"Lauricella hypergeometric series","level":5,"score":0.5003495216369629},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.4995608329772949},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48486265540122986},{"id":"https://openalex.org/C52704855","wikidata":"https://www.wikidata.org/wiki/Q1126603","display_name":"Elliptic integral","level":2,"score":0.48374056816101074},{"id":"https://openalex.org/C60400383","wikidata":"https://www.wikidata.org/wiki/Q17028407","display_name":"Hypergeometric identity","level":5,"score":0.4816257357597351},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4699309766292572},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.43845129013061523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28166890144348145},{"id":"https://openalex.org/C165175332","wikidata":"https://www.wikidata.org/wiki/Q5958021","display_name":"Hypergeometric function of a matrix argument","level":4,"score":0.27543169260025024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14415860176086426},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1118047833442688},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:0801.4137","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0801.4137","pdf_url":"https://arxiv.org/pdf/0801.4137","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.0801.4137","doi":"https://doi.org/10.48550/arxiv.0801.4137","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0801.4137","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0801.4137","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0801.4137","pdf_url":"https://arxiv.org/pdf/0801.4137","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1619414190","https://openalex.org/W1662817770","https://openalex.org/W1965724687","https://openalex.org/W1975017574","https://openalex.org/W1976597710","https://openalex.org/W1983444175","https://openalex.org/W1994151522","https://openalex.org/W2017455909","https://openalex.org/W2034292687","https://openalex.org/W2036272066","https://openalex.org/W2077027051","https://openalex.org/W2593034862","https://openalex.org/W2609618094","https://openalex.org/W3104751346","https://openalex.org/W3106444930","https://openalex.org/W3123698889"],"related_works":["https://openalex.org/W4297211345","https://openalex.org/W2141941567","https://openalex.org/W1842498742","https://openalex.org/W4286469665","https://openalex.org/W1976175304","https://openalex.org/W2963318968","https://openalex.org/W4297824691","https://openalex.org/W2496899735","https://openalex.org/W2078566267","https://openalex.org/W311409409"],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2],"family":[3],"of":[4,13,47],"continuous":[5],"biorthogonal":[6],"functions":[7],"related":[8],"to":[9,40],"an":[10],"elliptic":[11,26,45],"analogue":[12],"the":[14,25,30,37,41,48],"Gauss":[15],"hypergeometric":[16],"function.":[17],"The":[18],"key":[19],"tools":[20],"used":[21],"for":[22],"that":[23],"are":[24,52],"beta":[27],"integral":[28,31],"and":[29,44],"Bailey":[32],"chain":[33],"introduced":[34],"earlier":[35],"by":[36],"author.":[38],"Relations":[39],"Sklyanin":[42],"algebra":[43],"analogues":[46],"Faddeev":[49],"modular":[50],"double":[51],"discussed":[53],"in":[54],"detail.":[55]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
