Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2007120513', 'doi': 'https://doi.org/10.1007/bf00863422', 'title': 'A method for computing the coefficients in the product-sum formula of associated Legendre functions', 'display_name': 'A method for computing the coefficients in the product-sum formula of associated Legendre functions', 'publication_year': 1995, 'publication_date': '1995-11-01', 'ids': {'openalex': 'https://openalex.org/W2007120513', 'doi': 'https://doi.org/10.1007/bf00863422', 'mag': '2007120513'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/bf00863422', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210204015', 'display_name': 'Journal of Geodesy', 'issn_l': '0949-7714', 'issn': ['0949-7714', '1432-1394'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], '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': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5016235819', 'display_name': 'Cheinway Hwang', 'orcid': 'https://orcid.org/0000-0002-3322-353X'}, 'institutions': [{'id': 'https://openalex.org/I148366613', 'display_name': 'National Yang Ming Chiao Tung University', 'ror': 'https://ror.org/00se2k293', 'country_code': 'TW', 'type': 'education', 'lineage': ['https://openalex.org/I148366613']}], 'countries': ['TW'], 'is_corresponding': True, 'raw_author_name': 'Cheinway Hwang', 'raw_affiliation_strings': ['Department of Civil Engineering, National Chiao-Tung University, Hsinchu, Taiwan'], 'affiliations': [{'raw_affiliation_string': 'Department of Civil Engineering, National Chiao-Tung University, Hsinchu, Taiwan', 'institution_ids': ['https://openalex.org/I148366613']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5016235819'], 'corresponding_institution_ids': ['https://openalex.org/I148366613'], 'apc_list': {'value': 2590, 'currency': 'EUR', 'value_usd': 3390, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.32, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 11, 'citation_normalized_percentile': {'value': 0.636364, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 78, 'max': 79}, 'biblio': {'volume': '70', 'issue': '1-2', 'first_page': '110', 'last_page': '116'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12516', 'display_name': 'Cantorian-Fractal Theory of Quantum Physics', 'score': 0.9795, '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'}}, 'topics': [{'id': 'https://openalex.org/T12516', 'display_name': 'Cantorian-Fractal Theory of Quantum Physics', 'score': 0.9795, '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': 'Characterization of Chaotic Quantum Dynamics and Structures', 'score': 0.9323, '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/T10622', 'display_name': 'Foundations of Quantum Mechanics and Interpretations', 'score': 0.9213, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/legendre-function', 'display_name': 'Legendre function', 'score': 0.84330213}, {'id': 'https://openalex.org/keywords/associated-legendre-polynomials', 'display_name': 'Associated Legendre polynomials', 'score': 0.81865656}, {'id': 'https://openalex.org/keywords/legendre-wavelet', 'display_name': 'Legendre wavelet', 'score': 0.7789434}, {'id': 'https://openalex.org/keywords/legendre-transformation', 'display_name': 'Legendre transformation', 'score': 0.45413125}, {'id': 'https://openalex.org/keywords/lagrangian-coherent-structures', 'display_name': 'Lagrangian Coherent Structures', 'score': 0.400544}], 'concepts': [{'id': 'https://openalex.org/C111458787', 'wikidata': 'https://www.wikidata.org/wiki/Q215405', 'display_name': 'Legendre polynomials', 'level': 2, 'score': 0.9245558}, {'id': 'https://openalex.org/C153262748', 'wikidata': 'https://www.wikidata.org/wiki/Q17098449', 'display_name': 'Legendre function', 'level': 3, 'score': 0.84330213}, {'id': 'https://openalex.org/C36956377', 'wikidata': 'https://www.wikidata.org/wiki/Q228376', 'display_name': 'Associated Legendre polynomials', 'level': 5, 'score': 0.81865656}, {'id': 'https://openalex.org/C123769847', 'wikidata': 'https://www.wikidata.org/wiki/Q6517888', 'display_name': 'Legendre wavelet', 'level': 5, 'score': 0.7789434}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.72354895}, {'id': 'https://openalex.org/C86287605', 'wikidata': 'https://www.wikidata.org/wiki/Q4454970', 'display_name': "Legendre's equation", 'level': 3, 'score': 0.6525816}, {'id': 'https://openalex.org/C90673727', 'wikidata': 'https://www.wikidata.org/wiki/Q901718', 'display_name': 'Product (mathematics)', 'level': 2, 'score': 0.59379673}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.5691746}, {'id': 'https://openalex.org/C45374587', 'wikidata': 'https://www.wikidata.org/wiki/Q12525525', 'display_name': 'Computation', 'level': 2, 'score': 0.5391287}, {'id': 'https://openalex.org/C116594300', 'wikidata': 'https://www.wikidata.org/wiki/Q908652', 'display_name': 'Legendre transformation', 'level': 2, 'score': 0.45413125}, {'id': 'https://openalex.org/C90119067', 'wikidata': 'https://www.wikidata.org/wiki/Q43260', 'display_name': 'Polynomial', 'level': 2, 'score': 0.44945115}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.43552098}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.4164515}, {'id': 'https://openalex.org/C21736991', 'wikidata': 'https://www.wikidata.org/wiki/Q17006917', 'display_name': 'Classical orthogonal polynomials', 'level': 3, 'score': 0.2069116}, {'id': 'https://openalex.org/C10628310', 'wikidata': 'https://www.wikidata.org/wiki/Q619458', 'display_name': 'Orthogonal polynomials', 'level': 2, 'score': 0.16062135}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.14081886}, {'id': 'https://openalex.org/C78540521', 'wikidata': 'https://www.wikidata.org/wiki/Q1498246', 'display_name': 'Gegenbauer polynomials', 'level': 4, 'score': 0.12680438}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.11460057}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.11018798}, {'id': 'https://openalex.org/C46286280', 'wikidata': 'https://www.wikidata.org/wiki/Q2414958', 'display_name': 'Discrete wavelet transform', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C196216189', 'wikidata': 'https://www.wikidata.org/wiki/Q2867', 'display_name': 'Wavelet transform', 'level': 3, '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/C78458016', 'wikidata': 'https://www.wikidata.org/wiki/Q840400', 'display_name': 'Evolutionary biology', '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/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/bf00863422', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210204015', 'display_name': 'Journal of Geodesy', 'issn_l': '0949-7714', 'issn': ['0949-7714', '1432-1394'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 10, 'referenced_works': ['https://openalex.org/W1535035979', 'https://openalex.org/W1987940826', 'https://openalex.org/W2017723589', 'https://openalex.org/W2018824953', 'https://openalex.org/W2056162638', 'https://openalex.org/W2089328757', 'https://openalex.org/W2092646112', 'https://openalex.org/W2111333242', 'https://openalex.org/W4246936399', 'https://openalex.org/W4249790988'], 'related_works': ['https://openalex.org/W4246417956', 'https://openalex.org/W3020087995', 'https://openalex.org/W2953361964', 'https://openalex.org/W2891194680', 'https://openalex.org/W2736737644', 'https://openalex.org/W2379187670', 'https://openalex.org/W2217115449', 'https://openalex.org/W2025296287', 'https://openalex.org/W2022538265', 'https://openalex.org/W1607269076'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2007120513', 'counts_by_year': [{'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 3}, {'year': 2019, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 1}], 'updated_date': '2024-08-13T03:24:30.478774', 'created_date': '2016-06-24'}