{"id":"https://openalex.org/W1923074435","doi":"https://doi.org/10.18576/jant/040108","title":"New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers","display_name":"New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1923074435","doi":"https://doi.org/10.18576/jant/040108","mag":"1923074435"},"language":"en","primary_location":{"id":"doi:10.18576/jant/040108","doi":"https://doi.org/10.18576/jant/040108","is_oa":false,"landing_page_url":"https://doi.org/10.18576/jant/040108","pdf_url":null,"source":{"id":"https://openalex.org/S4210180010","display_name":"Journal of Analysis & Number Theory","issn_l":"2375-2785","issn":["2375-2785","2375-2807"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4353108630","host_organization_name":"Natural Sciences Publishing","host_organization_lineage":["https://openalex.org/P4353108630"],"host_organization_lineage_names":["Natural Sciences Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Analysis &amp; Number Theory","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1508.07345","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028280395","display_name":"Kunle Adegoke","orcid":"https://orcid.org/0000-0002-3933-0459","observed_orcids":["https://orcid.org/0000-0002-3933-0459"]},"institutions":[{"id":"https://openalex.org/I45711476","display_name":"Obafemi Awolowo University","ror":"https://ror.org/04snhqa82","country_code":"NG","type":"education","lineage":["https://openalex.org/I45711476"]}],"countries":["NG"],"is_corresponding":true,"raw_author_name":"Kunle Adegoke","raw_affiliation_strings":["Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife, 220005 Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife, 220005 Nigeria","institution_ids":["https://openalex.org/I45711476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048852325","display_name":"Olawanle P. Layeni","orcid":"https://orcid.org/0000-0002-2001-9943","observed_orcids":["https://orcid.org/0000-0002-2001-9943"]},"institutions":[{"id":"https://openalex.org/I45711476","display_name":"Obafemi Awolowo University","ror":"https://ror.org/04snhqa82","country_code":"NG","type":"education","lineage":["https://openalex.org/I45711476"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Olawanle Layeni","raw_affiliation_strings":["Department of Mathematics, Obafemi Awolowo University, Ile-Ife, 220005 Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Obafemi Awolowo University, Ile-Ife, 220005 Nigeria","institution_ids":["https://openalex.org/I45711476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028280395"],"corresponding_institution_ids":["https://openalex.org/I45711476"],"apc_list":null,"apc_paid":null,"fwci":0.5131,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.53697997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"4","issue":"1","first_page":"49","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9916999936103821,"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":"Advanced Mathematical Identities","score":0.9916999936103821,"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/T11166","display_name":"Analytic Number Theory Research","score":0.006899999920278788,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-harmonic-numbers","display_name":"generalized harmonic numbers","score":0.9940000176429749},{"id":"https://openalex.org/keywords/summation-identities","display_name":"summation identities","score":0.9819999933242798},{"id":"https://openalex.org/keywords/infinite-series","display_name":"infinite series","score":0.8510000109672546},{"id":"https://openalex.org/keywords/finite-sums","display_name":"finite sums","score":0.9879999756813049},{"id":"https://openalex.org/keywords/alternating-sums","display_name":"alternating sums","score":0.9190000295639038},{"id":"https://openalex.org/keywords/summation-formulas","display_name":"summation formulas","score":0.7900000214576721}],"concepts":[{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.7554538249969482},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.6819044947624207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6175839900970459},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.5849198698997498},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43806976079940796},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38657981157302856},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.310080349445343},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08134990930557251},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.052112698554992676}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.18576/jant/040108","doi":"https://doi.org/10.18576/jant/040108","is_oa":false,"landing_page_url":"https://doi.org/10.18576/jant/040108","pdf_url":null,"source":{"id":"https://openalex.org/S4210180010","display_name":"Journal of Analysis & Number Theory","issn_l":"2375-2785","issn":["2375-2785","2375-2807"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4353108630","host_organization_name":"Natural Sciences Publishing","host_organization_lineage":["https://openalex.org/P4353108630"],"host_organization_lineage_names":["Natural Sciences Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Analysis &amp; Number Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1508.07345","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.07345","pdf_url":"https://arxiv.org/pdf/1508.07345","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2963265574","doi":null,"is_oa":false,"landing_page_url":"https://www.vixra.org/pdf/1508.0204v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null},{"id":"doi:10.48550/arxiv.1508.07345","doi":"https://doi.org/10.48550/arxiv.1508.07345","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.07345","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1508.07345","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.07345","pdf_url":"https://arxiv.org/pdf/1508.07345","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1923074435.pdf","grobid_xml":"https://content.openalex.org/works/W1923074435.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1978792454","https://openalex.org/W1991273640","https://openalex.org/W2012652968","https://openalex.org/W2029948740","https://openalex.org/W2041231231","https://openalex.org/W2083779556","https://openalex.org/W2086986324","https://openalex.org/W2132156521","https://openalex.org/W2168668766","https://openalex.org/W2329095262"],"related_works":["https://openalex.org/W1981006054","https://openalex.org/W2088730553","https://openalex.org/W2148072272","https://openalex.org/W2025891270","https://openalex.org/W2895163320","https://openalex.org/W2132156521","https://openalex.org/W2964204797","https://openalex.org/W2584201203","https://openalex.org/W2567440453","https://openalex.org/W6885097123"],"abstract_inverted_index":{"We":[0],"state":[1],"and":[2,23,35,62],"prove":[3],"a":[4],"general":[5],"summation":[6,16,53,68],"identity.":[7],"The":[8,38],"identity":[9],"is":[10],"then":[11],"applied":[12],"to":[13],"derive":[14],"various":[15],"formulas":[17,69],"involving":[18,55,70],"the":[19,46,63],"generalized":[20,58],"harmonic":[21,59],"numbers":[22,72],"related":[24],"quantities.":[25],"Interesting":[26],"results,":[27],"mostly":[28],"new,":[29],"are":[30,44],"obtained":[31],"for":[32],"both":[33],"finite":[34],"infinite":[36,52],"sums.":[37],"high":[39],"points":[40],"of":[41,48,65],"this":[42],"paper":[43],"perhaps":[45],"discovery":[47],"several":[49],"previously":[50],"unknown":[51],"results":[54],"{\\em":[56],"non-linear}":[57],"number":[60],"terms":[61],"derivation":[64],"interesting":[66],"alternating":[67],"these":[71]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
