Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2010424411', 'doi': 'https://doi.org/10.1155/s1110757x03204101', 'title': 'A generalization of the Bernoulli polynomials', 'display_name': 'A generalization of the Bernoulli polynomials', 'publication_year': 2003, 'publication_date': '2003-01-01', 'ids': {'openalex': 'https://openalex.org/W2010424411', 'doi': 'https://doi.org/10.1155/s1110757x03204101', 'mag': '2010424411'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1155/s1110757x03204101', 'pdf_url': 'https://downloads.hindawi.com/journals/jam/2003/794908.pdf', 'source': {'id': 'https://openalex.org/S190082376', 'display_name': 'Journal of Applied Mathematics', 'issn_l': '1110-757X', 'issn': ['1110-757X', '1687-0042'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319869', 'host_organization_name': 'Hindawi Publishing Corporation', 'host_organization_lineage': ['https://openalex.org/P4310319869'], 'host_organization_lineage_names': ['Hindawi Publishing Corporation'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref', 'doaj'], 'open_access': {'is_oa': True, 'oa_status': 'gold', 'oa_url': 'https://downloads.hindawi.com/journals/jam/2003/794908.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5046705553', 'display_name': 'Pierpaolo Natalini', 'orcid': 'https://orcid.org/0000-0002-3862-8376'}, 'institutions': [{'id': 'https://openalex.org/I119003972', 'display_name': 'Roma Tre University', 'ror': 'https://ror.org/05vf0dg29', 'country_code': 'IT', 'type': 'education', 'lineage': ['https://openalex.org/I119003972']}], 'countries': ['IT'], 'is_corresponding': False, 'raw_author_name': 'Pierpaolo Natalini', 'raw_affiliation_strings': ['Dipartimento di Matematica, Università degli Studi Roma III, Largo San Leonardo Murialdo 1, Roma 00146'], 'affiliations': [{'raw_affiliation_string': 'Dipartimento di Matematica, Università degli Studi Roma III, Largo San Leonardo Murialdo 1, Roma 00146', 'institution_ids': ['https://openalex.org/I119003972']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5046403060', 'display_name': 'Angela Bernardini', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I88155538', 'display_name': 'Universidad de Navarra', 'ror': 'https://ror.org/02rxc7m23', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I88155538']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'Angela Bernardini', 'raw_affiliation_strings': ['Departamento de Fisica y Matemática Aplicada, Universidad de Navarra, Pamplona E-30080'], 'affiliations': [{'raw_affiliation_string': 'Departamento de Fisica y Matemática Aplicada, Universidad de Navarra, Pamplona E-30080', 'institution_ids': ['https://openalex.org/I88155538']}]}], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 1025, 'currency': 'USD', 'value_usd': 1025, 'provenance': 'doaj'}, 'apc_paid': {'value': 1025, 'currency': 'USD', 'value_usd': 1025, 'provenance': 'doaj'}, 'fwci': 1.236, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 78, 'citation_normalized_percentile': {'value': 0.953098, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 95, 'max': 96}, 'biblio': {'volume': '2003', 'issue': '3', 'first_page': '155', 'last_page': '163'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11428', 'display_name': 'Arithmetic of Multiple Zeta Values and Related Functions', 'score': 0.6184, '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'}}, 'topics': [{'id': 'https://openalex.org/T11428', 'display_name': 'Arithmetic of Multiple Zeta Values and Related Functions', 'score': 0.6184, '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/T11191', 'display_name': 'Orthogonal Polynomials', 'score': 0.5471, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/bernoulli-polynomials', 'display_name': 'Bernoulli polynomials', 'score': 0.7473906}, {'id': 'https://openalex.org/keywords/bernoulli-process', 'display_name': 'Bernoulli process', 'score': 0.6174705}, {'id': 'https://openalex.org/keywords/bernoulli-differential-equation', 'display_name': 'Bernoulli differential equation', 'score': 0.54893064}, {'id': 'https://openalex.org/keywords/matrix-valued-polynomials', 'display_name': 'Matrix Valued Polynomials', 'score': 0.490529}], 'concepts': [{'id': 'https://openalex.org/C177148314', 'wikidata': 'https://www.wikidata.org/wiki/Q170084', 'display_name': 'Generalization', 'level': 2, 'score': 0.82709306}, {'id': 'https://openalex.org/C196172290', 'wikidata': 'https://www.wikidata.org/wiki/Q2346201', 'display_name': 'Bernoulli polynomials', 'level': 4, 'score': 0.7473906}, {'id': 'https://openalex.org/C152361515', 'wikidata': 'https://www.wikidata.org/wiki/Q181328', 'display_name': "Bernoulli's principle", 'level': 2, 'score': 0.69241965}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.6775209}, {'id': 'https://openalex.org/C23990920', 'wikidata': 'https://www.wikidata.org/wiki/Q518831', 'display_name': 'Bernoulli process', 'level': 3, 'score': 0.6174705}, {'id': 'https://openalex.org/C37423430', 'wikidata': 'https://www.wikidata.org/wiki/Q6750281', 'display_name': 'Hull', 'level': 2, 'score': 0.5798368}, {'id': 'https://openalex.org/C187834632', 'wikidata': 'https://www.wikidata.org/wiki/Q188804', 'display_name': 'Factorization', 'level': 2, 'score': 0.5792947}, {'id': 'https://openalex.org/C76717707', 'wikidata': 'https://www.wikidata.org/wiki/Q793674', 'display_name': 'Bernoulli differential equation', 'level': 5, 'score': 0.54893064}, {'id': 'https://openalex.org/C93226319', 'wikidata': 'https://www.wikidata.org/wiki/Q193137', 'display_name': 'Differential (mechanical device)', 'level': 2, 'score': 0.51854426}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.39532816}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.3947693}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.3777944}, {'id': 'https://openalex.org/C78045399', 'wikidata': 'https://www.wikidata.org/wiki/Q11214', 'display_name': 'Differential equation', 'level': 2, 'score': 0.37433207}, {'id': 'https://openalex.org/C86607863', 'wikidata': 'https://www.wikidata.org/wiki/Q5275279', 'display_name': 'Difference polynomials', 'level': 3, 'score': 0.30956647}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.26892325}, {'id': 'https://openalex.org/C10628310', 'wikidata': 'https://www.wikidata.org/wiki/Q619458', 'display_name': 'Orthogonal polynomials', 'level': 2, 'score': 0.26567003}, {'id': 'https://openalex.org/C51544822', 'wikidata': 'https://www.wikidata.org/wiki/Q465274', 'display_name': 'Ordinary differential equation', 'level': 3, 'score': 0.18484294}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.1277085}, {'id': 'https://openalex.org/C186219872', 'wikidata': 'https://www.wikidata.org/wiki/Q955889', 'display_name': 'Differential algebraic equation', 'level': 4, 'score': 0.05970055}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.053637058}, {'id': 'https://openalex.org/C199104240', 'wikidata': 'https://www.wikidata.org/wiki/Q118291', 'display_name': 'Marine engineering', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C97355855', 'wikidata': 'https://www.wikidata.org/wiki/Q11473', 'display_name': 'Thermodynamics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1155/s1110757x03204101', 'pdf_url': 'https://downloads.hindawi.com/journals/jam/2003/794908.pdf', 'source': {'id': 'https://openalex.org/S190082376', 'display_name': 'Journal of Applied Mathematics', 'issn_l': '1110-757X', 'issn': ['1110-757X', '1687-0042'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319869', 'host_organization_name': 'Hindawi Publishing Corporation', 'host_organization_lineage': ['https://openalex.org/P4310319869'], 'host_organization_lineage_names': ['Hindawi Publishing Corporation'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': False, 'landing_page_url': 'https://doaj.org/article/8c795c39d15846c0a655c82198219f13', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306401280', 'display_name': 'DOAJ (DOAJ: Directory of Open Access Journals)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://projecteuclid.org/euclid.jam/1049725735', 'pdf_url': 'https://projecteuclid.org/journals/journal-of-applied-mathematics/volume-2003/issue-3/A-generalization-of-the-Bernoulli-polynomials/10.1155/S1110757X03204101.pdf', 'source': {'id': 'https://openalex.org/S4306400787', 'display_name': 'Project Euclid (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1155/s1110757x03204101', 'pdf_url': 'https://downloads.hindawi.com/journals/jam/2003/794908.pdf', 'source': {'id': 'https://openalex.org/S190082376', 'display_name': 'Journal of Applied Mathematics', 'issn_l': '1110-757X', 'issn': ['1110-757X', '1687-0042'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319869', 'host_organization_name': 'Hindawi Publishing Corporation', 'host_organization_lineage': ['https://openalex.org/P4310319869'], 'host_organization_lineage_names': ['Hindawi Publishing Corporation'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 11, 'referenced_works': ['https://openalex.org/W2009307604', 'https://openalex.org/W2024752843', 'https://openalex.org/W2049390370', 'https://openalex.org/W2049407028', 'https://openalex.org/W2076393035', 'https://openalex.org/W2299769372', 'https://openalex.org/W2414055905', 'https://openalex.org/W2787959293', 'https://openalex.org/W4230941884', 'https://openalex.org/W4385393758', 'https://openalex.org/W604181985'], 'related_works': ['https://openalex.org/W3089400922', 'https://openalex.org/W2978189732', 'https://openalex.org/W2899588557', 'https://openalex.org/W2765544567', 'https://openalex.org/W2381814360', 'https://openalex.org/W2355356365', 'https://openalex.org/W2123713498', 'https://openalex.org/W1991879433', 'https://openalex.org/W1674853208', 'https://openalex.org/W15241613'], 'abstract_inverted_index': {'A': [0], 'generalization': [1], 'of': [2, 8, 23, 27, 33], 'the': [3, 9, 20, 34], 'Bernoulli': [4, 10], 'polynomials': [5, 28], 'and,': [6], 'consequently,': [7], 'numbers,': [11], 'is': [12], 'defined': [13], 'starting': [14], 'from': [15], 'suitable': [16], 'generating': [17], 'functions.': [18], 'Furthermore,': [19], 'differential': [21], 'equations': [22], 'these': [24], 'new': [25], 'classes': [26], 'are': [29], 'derived': [30], 'by': [31, 38], 'means': [32], 'factorization': [35], 'method': [36], 'introduced': [37], 'Infeld': [39], 'and': [40], 'Hull': [41], '(1951).': [42]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2010424411', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 3}, {'year': 2022, 'cited_by_count': 6}, {'year': 2021, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 11}, {'year': 2019, 'cited_by_count': 5}, {'year': 2018, 'cited_by_count': 5}, {'year': 2017, 'cited_by_count': 3}, {'year': 2016, 'cited_by_count': 6}, {'year': 2015, 'cited_by_count': 7}, {'year': 2014, 'cited_by_count': 7}, {'year': 2013, 'cited_by_count': 7}, {'year': 2012, 'cited_by_count': 5}], 'updated_date': '2024-09-13T19:37:35.095806', 'created_date': '2016-06-24'}