{"id":"https://openalex.org/W2079919311","doi":"https://doi.org/10.1155/2008/794181","title":"Sums of Reciprocals of Triple Binomial Coefficients","display_name":"Sums of Reciprocals of Triple Binomial Coefficients","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2079919311","doi":"https://doi.org/10.1155/2008/794181","mag":"2079919311"},"language":"en","primary_location":{"id":"doi:10.1155/2008/794181","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/794181","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2008/794181.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2008/794181.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033061138","display_name":"Anthony Sofo","orcid":"https://orcid.org/0000-0002-1277-8296"},"institutions":[{"id":"https://openalex.org/I71270174","display_name":"Victoria University","ror":"https://ror.org/04j757h98","country_code":"AU","type":"education","lineage":["https://openalex.org/I71270174"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"A. Sofo","raw_affiliation_strings":["School of Computer Science and Mathematics, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia","Victoria University, Australia,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Mathematics, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia","institution_ids":["https://openalex.org/I71270174"]},{"raw_affiliation_string":"Victoria University, Australia,","institution_ids":["https://openalex.org/I71270174"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033061138"],"corresponding_institution_ids":["https://openalex.org/I71270174"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":2.1191,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.85703186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2008","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"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":1.0,"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":0.9998000264167786,"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":0.9994999766349792,"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/mathematics","display_name":"Mathematics","score":0.917856752872467},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.8785259127616882},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.6327093243598938},{"id":"https://openalex.org/keywords/binomial-theorem","display_name":"Binomial theorem","score":0.5955906510353088},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.548134982585907},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.503117024898529},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.4583415985107422},{"id":"https://openalex.org/keywords/central-binomial-coefficient","display_name":"Central binomial coefficient","score":0.4327566921710968},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.3771846294403076},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32603082060813904},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3225439190864563},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2989007234573364},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.08024284243583679},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.04424518346786499}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.917856752872467},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.8785259127616882},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.6327093243598938},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.5955906510353088},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.548134982585907},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.503117024898529},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.4583415985107422},{"id":"https://openalex.org/C134087691","wikidata":"https://www.wikidata.org/wiki/Q1045966","display_name":"Central binomial coefficient","level":4,"score":0.4327566921710968},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.3771846294403076},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32603082060813904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3225439190864563},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2989007234573364},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.08024284243583679},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.04424518346786499},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2008/794181","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/794181","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2008/794181.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:eprints.vu.edu.au:3966","is_oa":false,"landing_page_url":"https://vuir.vu.edu.au/3966/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400215","display_name":"Victoria University Research Repository (Victoria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I41156924","host_organization_name":"Victoria University of Wellington","host_organization_lineage":["https://openalex.org/I41156924"],"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":"Article"},{"id":"pmh:oai:RePEc:hin:jijmms:794181","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2008/794181.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:c5970453d1ba456e8d7d5902c59308f0","is_oa":true,"landing_page_url":"https://doaj.org/article/c5970453d1ba456e8d7d5902c59308f0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2008 (2008)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2008/794181","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/794181","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2008/794181.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2079919311.pdf","grobid_xml":"https://content.openalex.org/works/W2079919311.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W69742356","https://openalex.org/W1504435277","https://openalex.org/W1515754334","https://openalex.org/W1842498742","https://openalex.org/W1964070782","https://openalex.org/W2039362637","https://openalex.org/W2044671577","https://openalex.org/W2105178121","https://openalex.org/W2328425686","https://openalex.org/W3104060427","https://openalex.org/W4241654653","https://openalex.org/W4254961642"],"related_works":["https://openalex.org/W2952300770","https://openalex.org/W4225635267","https://openalex.org/W3214798365","https://openalex.org/W2780957143","https://openalex.org/W2047523883","https://openalex.org/W4320152868","https://openalex.org/W4282583869","https://openalex.org/W2020662961","https://openalex.org/W3081861082","https://openalex.org/W2955220190"],"abstract_inverted_index":{"We":[0,15],"investigate":[1],"the":[2,9,26],"integral":[3],"representation":[4],"of":[5,11,21,28],"infinite":[6],"sums":[7],"involving":[8],"reciprocals":[10],"triple":[12],"binomial":[13],"coefficients.":[14],"also":[16],"recover":[17],"some":[18],"wellknown":[19],"properties":[20],"\u03b6":[22],"(3)":[23],"and":[24],"extend":[25],"range":[27],"results":[29],"given":[30],"by":[31],"other":[32],"authors.":[33]},"counts_by_year":[],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}