{"id":"https://openalex.org/W1990946273","doi":"https://doi.org/10.1016/s0012-365x(02)00584-8","title":"Some identities related to reciprocal functions","display_name":"Some identities related to reciprocal functions","publication_year":2003,"publication_date":"2003-04-01","ids":{"openalex":"https://openalex.org/W1990946273","doi":"https://doi.org/10.1016/s0012-365x(02)00584-8","mag":"1990946273"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(02)00584-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(02)00584-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109116247","display_name":"Xiqiang Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]},{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiqiang Zhao","raw_affiliation_strings":["Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 210016, People's Republic of China","Department of Mathematics, Shandong Institute of Technology, Zibo Shandong 255012, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 210016, People's Republic of China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Department of Mathematics, Shandong Institute of Technology, Zibo Shandong 255012, People's Republic of China","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100762626","display_name":"Tianming Wang","orcid":"https://orcid.org/0000-0001-8737-8310"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianming Wang","raw_affiliation_strings":["Department of Applied Mathematics, Dalian University of Technology, Dalian Liaoning 116024, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, Dalian Liaoning 116024, People's Republic of China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109116247"],"corresponding_institution_ids":["https://openalex.org/I119203015","https://openalex.org/I9842412"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":2.2103,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.8385947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"265","issue":"1-3","first_page":"323","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9850000143051147,"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":"Mathematical functions and polynomials","score":0.958299994468689,"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/reciprocal","display_name":"Reciprocal","score":0.9135401248931885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.894949197769165},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.8417423367500305},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-second-kind","display_name":"Stirling numbers of the second kind","score":0.8044090270996094},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-first-kind","display_name":"Stirling numbers of the first kind","score":0.6766175627708435},{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.6719774007797241},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.5542433261871338},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46343594789505005},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42655813694000244},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08407539129257202}],"concepts":[{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.9135401248931885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.894949197769165},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.8417423367500305},{"id":"https://openalex.org/C2284495","wikidata":"https://www.wikidata.org/wiki/Q2601117","display_name":"Stirling numbers of the second kind","level":2,"score":0.8044090270996094},{"id":"https://openalex.org/C93765064","wikidata":"https://www.wikidata.org/wiki/Q2657556","display_name":"Stirling numbers of the first kind","level":3,"score":0.6766175627708435},{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.6719774007797241},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.5542433261871338},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46343594789505005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42655813694000244},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08407539129257202},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(02)00584-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(02)00584-8","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.49000000953674316,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4293439290","https://openalex.org/W2441714773","https://openalex.org/W1751837709","https://openalex.org/W2950221119","https://openalex.org/W2060935821","https://openalex.org/W4293437882","https://openalex.org/W1555608773","https://openalex.org/W3024002232","https://openalex.org/W4302413018","https://openalex.org/W17723721"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":5}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}