Recurrence relations for discrete hypergeometric functions

Name: Work Video:
Duration: 3 min 30 s
Description: We present a general procedure for finding linear recurrence relations for the solutions of the second order difference equation of hypergeometric type. Applications to wave functions of certain discrete system are also given.
R. Álvarez-Nodarse; J. L. Cardoso
{'id': 'https://openalex.org/W2079055545', 'doi': 'https://doi.org/10.1080/10236190500089846', 'title': 'Recurrence relations for discrete hypergeometric functions', 'display_name': 'Recurrence relations for discrete hypergeometric functions', 'publication_year': 2005, 'publication_date': '2005-08-01', 'ids': {'openalex': 'https://openalex.org/W2079055545', 'doi': 'https://doi.org/10.1080/10236190500089846', 'mag': '2079055545'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1080/10236190500089846', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S137349598', 'display_name': 'The Journal of Difference Equations and Applications', 'issn_l': '1023-6198', 'issn': ['1023-6198', '1026-7042', '1563-5120'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320547', 'host_organization_name': 'Taylor & Francis', 'host_organization_lineage': ['https://openalex.org/P4310320547'], 'host_organization_lineage_names': ['Taylor & Francis'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://idus.us.es/bitstream/11441/41747/1/Recurrence%20relations%20for%20discrete%20hypergeometric%20functions.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5074814332', 'display_name': 'R. Álvarez-Nodarse', 'orcid': 'https://orcid.org/0000-0002-9038-4698'}, 'institutions': [{'id': 'https://openalex.org/I173304897', 'display_name': 'Universidad de Granada', 'ror': 'https://ror.org/04njjy449', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I173304897']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'R. Álvarez-Nodarse', 'raw_affiliation_strings': ['b  Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada ,  E-18071 ,  Granada ,  Spain'], 'affiliations': [{'raw_affiliation_string': 'b  Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada ,  E-18071 ,  Granada ,  Spain', 'institution_ids': ['https://openalex.org/I173304897']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5011005464', 'display_name': 'J. L. Cardoso', 'orcid': 'https://orcid.org/0000-0002-7418-3634'}, 'institutions': [{'id': 'https://openalex.org/I155381812', 'display_name': 'University of Trás-os-Montes and Alto Douro', 'ror': 'https://ror.org/03qc8vh97', 'country_code': 'PT', 'type': 'education', 'lineage': ['https://openalex.org/I155381812']}], 'countries': ['PT'], 'is_corresponding': False, 'raw_author_name': 'J.L. Cardoso', 'raw_affiliation_strings': ['c  Universidade de Trás-os-Montes e Alto Douro,  Departamento de Matemática  , Apartado 202,  5001-911 ,  Vila Real ,  Portugal'], 'affiliations': [{'raw_affiliation_string': 'c  Universidade de Trás-os-Montes e Alto Douro,  Departamento de Matemática  , Apartado 202,  5001-911 ,  Vila Real ,  Portugal', 'institution_ids': ['https://openalex.org/I155381812']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.19, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 7, 'citation_normalized_percentile': {'value': 0.636403, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 79, 'max': 80}, 'biblio': {'volume': '11', 'issue': '9', 'first_page': '829', 'last_page': '850'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11262', 'display_name': 'Quantum Mechanics and Non-Hermitian Physics', 'score': 0.9997, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11262', 'display_name': 'Quantum Mechanics and Non-Hermitian Physics', 'score': 0.9997, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10248', 'display_name': 'Nonlinear Waves and Solitons', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11261', 'display_name': 'Quantum chaos and dynamical systems', 'score': 0.9958, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/recurrence-relation', 'display_name': 'Recurrence relation', 'score': 0.75073326}, {'id': 'https://openalex.org/keywords/hypergeometric-distribution', 'display_name': 'Hypergeometric distribution', 'score': 0.7009554}, {'id': 'https://openalex.org/keywords/basic-hypergeometric-series', 'display_name': 'Basic hypergeometric series', 'score': 0.6575539}, {'id': 'https://openalex.org/keywords/bilateral-hypergeometric-series', 'display_name': 'Bilateral hypergeometric series', 'score': 0.54853106}, {'id': 'https://openalex.org/keywords/hypergeometric-identity', 'display_name': 'Hypergeometric identity', 'score': 0.43649444}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8812746}, {'id': 'https://openalex.org/C201292218', 'wikidata': 'https://www.wikidata.org/wiki/Q740970', 'display_name': 'Recurrence relation', 'level': 2, 'score': 0.75073326}, {'id': 'https://openalex.org/C158241908', 'wikidata': 'https://www.wikidata.org/wiki/Q109744257', 'display_name': 'Generalized hypergeometric function', 'level': 3, 'score': 0.7090248}, {'id': 'https://openalex.org/C176671685', 'wikidata': 'https://www.wikidata.org/wiki/Q730600', 'display_name': 'Hypergeometric distribution', 'level': 2, 'score': 0.7009554}, {'id': 'https://openalex.org/C92941272', 'wikidata': 'https://www.wikidata.org/wiki/Q1062958', 'display_name': 'Basic hypergeometric series', 'level': 3, 'score': 0.6575539}, {'id': 'https://openalex.org/C197320386', 'wikidata': 'https://www.wikidata.org/wiki/Q21028472', 'display_name': 'Hypergeometric function', 'level': 2, 'score': 0.6528836}, {'id': 'https://openalex.org/C148160416', 'wikidata': 'https://www.wikidata.org/wiki/Q783948', 'display_name': 'Confluent hypergeometric function', 'level': 3, 'score': 0.57613397}, {'id': 'https://openalex.org/C182078607', 'wikidata': 'https://www.wikidata.org/wiki/Q4907583', 'display_name': 'Bilateral hypergeometric series', 'level': 5, 'score': 0.54853106}, {'id': 'https://openalex.org/C2777299769', 'wikidata': 'https://www.wikidata.org/wiki/Q3707858', 'display_name': 'Type (biology)', 'level': 2, 'score': 0.51767635}, {'id': 'https://openalex.org/C165175332', 'wikidata': 'https://www.wikidata.org/wiki/Q5958021', 'display_name': 'Hypergeometric function of a matrix argument', 'level': 4, 'score': 0.49523035}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.47174725}, {'id': 'https://openalex.org/C60400383', 'wikidata': 'https://www.wikidata.org/wiki/Q17028407', 'display_name': 'Hypergeometric identity', 'level': 5, 'score': 0.43649444}, {'id': 'https://openalex.org/C182306322', 'wikidata': 'https://www.wikidata.org/wiki/Q1779371', 'display_name': 'Order (exchange)', 'level': 2, 'score': 0.4138787}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.350551}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.32428056}, {'id': 'https://openalex.org/C18903297', 'wikidata': 'https://www.wikidata.org/wiki/Q7150', 'display_name': 'Ecology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C10138342', 'wikidata': 'https://www.wikidata.org/wiki/Q43015', 'display_name': 'Finance', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1080/10236190500089846', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S137349598', 'display_name': 'The Journal of Difference Equations and Applications', 'issn_l': '1023-6198', 'issn': ['1023-6198', '1026-7042', '1563-5120'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320547', 'host_organization_name': 'Taylor & Francis', 'host_organization_lineage': ['https://openalex.org/P4310320547'], 'host_organization_lineage_names': ['Taylor & Francis'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://idus.us.es/handle/11441/41747', 'pdf_url': 'https://idus.us.es/bitstream/11441/41747/1/Recurrence%20relations%20for%20discrete%20hypergeometric%20functions.pdf', 'source': {'id': 'https://openalex.org/S4306402641', 'display_name': 'LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4383465926', 'host_organization_name': 'LA Referencia', 'host_organization_lineage': ['https://openalex.org/I4383465926'], 'host_organization_lineage_names': ['LA Referencia'], 'type': 'repository'}, 'license': 'cc-by-nc-nd', 'license_id': 'https://openalex.org/licenses/cc-by-nc-nd', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://idus.us.es/handle/11441/41747', 'pdf_url': 'https://idus.us.es/bitstream/11441/41747/1/Recurrence%20relations%20for%20discrete%20hypergeometric%20functions.pdf', 'source': {'id': 'https://openalex.org/S4306402641', 'display_name': 'LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4383465926', 'host_organization_name': 'LA Referencia', 'host_organization_lineage': ['https://openalex.org/I4383465926'], 'host_organization_lineage_names': ['LA Referencia'], 'type': 'repository'}, 'license': 'cc-by-nc-nd', 'license_id': 'https://openalex.org/licenses/cc-by-nc-nd', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 25, 'referenced_works': ['https://openalex.org/W1528387448', 'https://openalex.org/W1597051923', 'https://openalex.org/W1654411218', 'https://openalex.org/W190006759', 'https://openalex.org/W1964107355', 'https://openalex.org/W1970717102', 'https://openalex.org/W1979887955', 'https://openalex.org/W1992325098', 'https://openalex.org/W2013244555', 'https://openalex.org/W2028287891', 'https://openalex.org/W2030046855', 'https://openalex.org/W2043293029', 'https://openalex.org/W2053857014', 'https://openalex.org/W2072740780', 'https://openalex.org/W2085189989', 'https://openalex.org/W2091271174', 'https://openalex.org/W2151063832', 'https://openalex.org/W2160625162', 'https://openalex.org/W2161446160', 'https://openalex.org/W2170980473', 'https://openalex.org/W3037568975', 'https://openalex.org/W3091798827', 'https://openalex.org/W3100126901', 'https://openalex.org/W4239108367', 'https://openalex.org/W4300879736'], 'related_works': ['https://openalex.org/W4320858047', 'https://openalex.org/W4307312159', 'https://openalex.org/W4306867421', 'https://openalex.org/W3126885930', 'https://openalex.org/W2949895432', 'https://openalex.org/W2801577962', 'https://openalex.org/W2602012601', 'https://openalex.org/W21025452', 'https://openalex.org/W2092389177', 'https://openalex.org/W2070204410'], 'abstract_inverted_index': {'We': [0], 'present': [1], 'a': [2], 'general': [3], 'procedure': [4], 'for': [5, 10], 'finding': [6], 'linear': [7], 'recurrence': [8], 'relations': [9], 'the': [11, 14], 'solutions': [12], 'of': [13, 19, 26], 'second': [15], 'order': [16], 'difference': [17], 'equation': [18], 'hypergeometric': [20], 'type.': [21], 'Applications': [22], 'to': [23], 'wave': [24], 'functions': [25], 'certain': [27], 'discrete': [28], 'system': [29], 'are': [30], 'also': [31], 'given.': [32]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2079055545', 'counts_by_year': [{'year': 2020, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 1}], 'updated_date': '2024-12-16T12:37:16.760116', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
