{"id":"https://openalex.org/W14107349","doi":"https://doi.org/10.1007/978-1-4613-9647-5_2","title":"Summation of Harmonic Numbers","display_name":"Summation of Harmonic Numbers","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W14107349","doi":"https://doi.org/10.1007/978-1-4613-9647-5_2","mag":"14107349"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4613-9647-5_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_2","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"},"type":"book-chapter","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/A5053931149","display_name":"Dominic Y. Savio","orcid":null},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dominic Y. Savio","raw_affiliation_strings":["Department of Computer Science and Statistics, The University of Rhode Island, Kingston, Rhode Island, 02881, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Statistics, The University of Rhode Island, Kingston, Rhode Island, 02881, USA","institution_ids":["https://openalex.org/I17626003"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017474781","display_name":"Edmund A. Lamagna","orcid":null},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edmund A. Lamagna","raw_affiliation_strings":["Department of Computer Science and Statistics, The University of Rhode Island, Kingston, Rhode Island, 02881, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Statistics, The University of Rhode Island, Kingston, Rhode Island, 02881, USA","institution_ids":["https://openalex.org/I17626003"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075118151","display_name":"Shing-Min Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shing-Min Liu","raw_affiliation_strings":["Department of Computer Science and Statistics, The University of Rhode Island, Kingston, Rhode Island, 02881, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Statistics, The University of Rhode Island, Kingston, Rhode Island, 02881, USA","institution_ids":["https://openalex.org/I17626003"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053931149"],"corresponding_institution_ids":["https://openalex.org/I17626003"],"apc_list":null,"apc_paid":null,"fwci":1.1246,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74014599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"12","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.3116999864578247,"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":"Advanced Mathematical Theories and Applications","score":0.3116999864578247,"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/harmonic","display_name":"Harmonic","score":0.7136760354042053},{"id":"https://openalex.org/keywords/harmonic-number","display_name":"Harmonic number","score":0.706551194190979},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.692511796951294},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6051574945449829},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.540444016456604},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.438963919878006},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.38782867789268494},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3465549349784851},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33888280391693115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33739709854125977},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18005988001823425},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14653950929641724},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.0662102997303009}],"concepts":[{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.7136760354042053},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.706551194190979},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.692511796951294},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6051574945449829},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.540444016456604},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.438963919878006},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.38782867789268494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3465549349784851},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33888280391693115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33739709854125977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18005988001823425},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14653950929641724},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0662102997303009},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4613-9647-5_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_2","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W293827664","https://openalex.org/W1978350736","https://openalex.org/W1983693613","https://openalex.org/W1993449345","https://openalex.org/W2029948740","https://openalex.org/W2067240242","https://openalex.org/W2128817474","https://openalex.org/W2153531485","https://openalex.org/W2568753013","https://openalex.org/W2752853835","https://openalex.org/W3145991194","https://openalex.org/W4247557026","https://openalex.org/W6610430299","https://openalex.org/W6780294949"],"related_works":["https://openalex.org/W1981006054","https://openalex.org/W2360188928","https://openalex.org/W2074912571","https://openalex.org/W4313447743","https://openalex.org/W4297813172","https://openalex.org/W3038180736","https://openalex.org/W2468623746","https://openalex.org/W1976244396","https://openalex.org/W3016847968","https://openalex.org/W2057404757"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}