Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1963912938', 'doi': 'https://doi.org/10.2478/s12175-013-0109-2', 'title': 'A completely monotonic function involving the tri- and tetra-gamma functions', 'display_name': 'A completely monotonic function involving the tri- and tetra-gamma functions', 'publication_year': 2013, 'publication_date': '2013-06-01', 'ids': {'openalex': 'https://openalex.org/W1963912938', 'doi': 'https://doi.org/10.2478/s12175-013-0109-2', 'mag': '1963912938'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2478/s12175-013-0109-2', 'pdf_url': 'http://www.degruyter.com/downloadpdf/j/ms.2013.63.issue-3/s12175-013-0109-2/s12175-013-0109-2.xml', 'source': {'id': 'https://openalex.org/S78192177', 'display_name': 'Mathematica Slovaca', 'issn_l': '0139-9918', 'issn': ['0139-9918', '1337-2211'], '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': 'cc-by-nc-nd', 'license_id': 'https://openalex.org/licenses/cc-by-nc-nd', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'hybrid', 'oa_url': 'http://www.degruyter.com/downloadpdf/j/ms.2013.63.issue-3/s12175-013-0109-2/s12175-013-0109-2.xml', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5073122046', 'display_name': 'Bai‐Ni Guo', 'orcid': 'https://orcid.org/0000-0001-6156-2590'}, 'institutions': [{'id': 'https://openalex.org/I4210166499', 'display_name': 'Henan Polytechnic University', 'ror': 'https://ror.org/05vr1c885', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I4210166499']}], 'countries': ['CN'], 'is_corresponding': True, 'raw_author_name': 'Bai-Ni Guo', 'raw_affiliation_strings': ['School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China', 'institution_ids': ['https://openalex.org/I4210166499']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5100695390', 'display_name': 'Feng Qi', 'orcid': 'https://orcid.org/0000-0001-6239-2968'}, 'institutions': [{'id': 'https://openalex.org/I3133090473', 'display_name': 'Weinan Normal University', 'ror': 'https://ror.org/00n2kc060', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I3133090473']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Jiao-Lian Zhao', 'raw_affiliation_strings': ['Department of Mathematics and Informatics, Weinan Teachers University, Weinan City, Shaanxi Province, 714000, China'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics and Informatics, Weinan Teachers University, Weinan City, Shaanxi Province, 714000, China', 'institution_ids': ['https://openalex.org/I3133090473']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5100695390', 'display_name': 'Feng Qi', 'orcid': 'https://orcid.org/0000-0001-6239-2968'}, 'institutions': [{'id': 'https://openalex.org/I4210166499', 'display_name': 'Henan Polytechnic University', 'ror': 'https://ror.org/05vr1c885', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I4210166499']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Feng Qi', 'raw_affiliation_strings': ['School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China', 'institution_ids': ['https://openalex.org/I4210166499']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': ['https://openalex.org/A5073122046'], 'corresponding_institution_ids': ['https://openalex.org/I4210166499'], 'apc_list': None, 'apc_paid': None, 'fwci': 3.378, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 18, 'citation_normalized_percentile': {'value': 0.835676, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 89, 'max': 90}, 'biblio': {'volume': '63', 'issue': '3', 'first_page': '469', 'last_page': '478'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11564', 'display_name': 'Matrix Inequalities and Geometric Means', 'score': 0.9999, '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/T11564', 'display_name': 'Matrix Inequalities and Geometric Means', 'score': 0.9999, '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/T12508', 'display_name': 'Stability of Functional Equations in Mathematical Analysis', 'score': 0.9993, '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/T11191', 'display_name': 'Orthogonal Polynomials', 'score': 0.9824, '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/gamma-function', 'display_name': 'Gamma Function', 'score': 0.554073}, {'id': 'https://openalex.org/keywords/tetra', 'display_name': 'Tetra', 'score': 0.41955158}], 'concepts': [{'id': 'https://openalex.org/C72169020', 'wikidata': 'https://www.wikidata.org/wiki/Q194404', 'display_name': 'Monotonic function', 'level': 2, 'score': 0.92537284}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7749869}, {'id': 'https://openalex.org/C82240120', 'wikidata': 'https://www.wikidata.org/wiki/Q190573', 'display_name': 'Gamma function', 'level': 2, 'score': 0.76113176}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.64166206}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.47313777}, {'id': 'https://openalex.org/C2777873363', 'wikidata': 'https://www.wikidata.org/wiki/Q13533436', 'display_name': 'Tetra', 'level': 2, 'score': 0.41955158}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.32299608}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.29289544}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.09661752}, {'id': 'https://openalex.org/C155647269', 'wikidata': 'https://www.wikidata.org/wiki/Q243455', 'display_name': 'Medicinal chemistry', 'level': 1, 'score': 0.046421677}, {'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/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.2478/s12175-013-0109-2', 'pdf_url': 'http://www.degruyter.com/downloadpdf/j/ms.2013.63.issue-3/s12175-013-0109-2/s12175-013-0109-2.xml', 'source': {'id': 'https://openalex.org/S78192177', 'display_name': 'Mathematica Slovaca', 'issn_l': '0139-9918', 'issn': ['0139-9918', '1337-2211'], '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': 'cc-by-nc-nd', 'license_id': 'https://openalex.org/licenses/cc-by-nc-nd', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1001.4611', 'pdf_url': 'https://arxiv.org/pdf/1001.4611', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (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': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': None, 'pdf_url': 'https://arxiv.org/pdf/1001.4611.pdf', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (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': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1001.4611', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2478/s12175-013-0109-2', 'pdf_url': 'http://www.degruyter.com/downloadpdf/j/ms.2013.63.issue-3/s12175-013-0109-2/s12175-013-0109-2.xml', 'source': {'id': 'https://openalex.org/S78192177', 'display_name': 'Mathematica Slovaca', 'issn_l': '0139-9918', 'issn': ['0139-9918', '1337-2211'], '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': 'cc-by-nc-nd', 'license_id': 'https://openalex.org/licenses/cc-by-nc-nd', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [{'id': 'https://metadata.un.org/sdg/10', 'display_name': 'Reduced inequalities', 'score': 0.41}], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W1963912938', 'https://openalex.org/W3099251211'], 'referenced_works_count': 17, 'referenced_works': ['https://openalex.org/W109103158', 'https://openalex.org/W1560063022', 'https://openalex.org/W1590460147', 'https://openalex.org/W1670149396', 'https://openalex.org/W1993522052', 'https://openalex.org/W2003813852', 'https://openalex.org/W2015649080', 'https://openalex.org/W2034424857', 'https://openalex.org/W2049461687', 'https://openalex.org/W2076748548', 'https://openalex.org/W2078914525', 'https://openalex.org/W2117885262', 'https://openalex.org/W2138025664', 'https://openalex.org/W2611779419', 'https://openalex.org/W2798198027', 'https://openalex.org/W2801179766', 'https://openalex.org/W2991854428'], 'related_works': ['https://openalex.org/W4287808774', 'https://openalex.org/W3106530133', 'https://openalex.org/W3103046732', 'https://openalex.org/W3098325605', 'https://openalex.org/W3021649813', 'https://openalex.org/W2950472823', 'https://openalex.org/W2949622191', 'https://openalex.org/W2779947287', 'https://openalex.org/W2081972949', 'https://openalex.org/W1761810493'], 'abstract_inverted_index': {'The': [0], 'psi': [1], 'function': [2, 29], '$\\psi(x)$': [3], 'is': [4, 18, 41], 'defined': [5], 'by': [6], "$\\psi(x)=\\frac{\\Gamma'(x)}{\\Gamma(x)}$": [7], 'and': [8, 35], '$\\psi^{(i)}(x)$': [9], 'for': [10], '$i\\in\\mathbb{N}$': [11], 'denote': [12], 'the': [13, 19, 31], 'polygamma': [14], 'functions,': [15], 'where': [16], '$\\Gamma(x)$': [17], 'gamma': [20], 'function.': [21], 'In': [22], 'this': [23], 'paper': [24], 'we': [25], 'prove': [26], 'that': [27], 'a': [28, 36], 'involving': [30], 'difference': [32], 'between': [33], "$[\\psi'(x)]^2+\\psi''(x)$": [34], 'proper': [37], 'fraction': [38], 'of': [39], '$x$': [40], 'completely': [42], 'monotonic': [43], 'on': [44], '$(0,\\infty)$.': [45]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1963912938', 'counts_by_year': [{'year': 2022, 'cited_by_count': 2}, {'year': 2020, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 2}, {'year': 2015, 'cited_by_count': 3}, {'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 4}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-09-08T11:35:08.187169', 'created_date': '2016-06-24'}