{"id":"https://openalex.org/W2038181734","doi":"https://doi.org/10.1145/1394042.1394052","title":"The q-WZ method for infinite sums (abstract only)","display_name":"The q-WZ method for infinite sums (abstract only)","publication_year":2008,"publication_date":"2008-07-25","ids":{"openalex":"https://openalex.org/W2038181734","doi":"https://doi.org/10.1145/1394042.1394052","mag":"2038181734"},"language":"en","primary_location":{"id":"doi:10.1145/1394042.1394052","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1394042.1394052","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","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/A5074795333","display_name":"William Y. C. Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"William Y.C. Chen","raw_affiliation_strings":["Nankai University, Tianjin, Peoples Rep of China"],"affiliations":[{"raw_affiliation_string":"Nankai University, Tianjin, Peoples Rep of China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042804126","display_name":"Ernest X. W. Xia","orcid":"https://orcid.org/0000-0002-9484-5156"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ernest X.W. Xia","raw_affiliation_strings":["Nankai University, Tianjin, Peoples Rep of China"],"affiliations":[{"raw_affiliation_string":"Nankai University, Tianjin, Peoples Rep of China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074795333"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12756985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"1-2","first_page":"19","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9908000230789185,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9639000296592712,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7370688915252686},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.6640490293502808},{"id":"https://openalex.org/keywords/gauss-sum","display_name":"Gauss sum","score":0.6061676740646362},{"id":"https://openalex.org/keywords/basic-hypergeometric-series","display_name":"Basic hypergeometric series","score":0.5901936888694763},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5821261405944824},{"id":"https://openalex.org/keywords/telescoping-series","display_name":"Telescoping series","score":0.5816873908042908},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.5444056987762451},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4866841435432434},{"id":"https://openalex.org/keywords/hypergeometric-identity","display_name":"Hypergeometric identity","score":0.45819908380508423},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45138129591941833},{"id":"https://openalex.org/keywords/hypergeometric-distribution","display_name":"Hypergeometric distribution","score":0.44782885909080505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4400918185710907},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3926185965538025},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.366299033164978},{"id":"https://openalex.org/keywords/generalized-hypergeometric-function","display_name":"Generalized hypergeometric function","score":0.3313373327255249},{"id":"https://openalex.org/keywords/hypergeometric-function-of-a-matrix-argument","display_name":"Hypergeometric function of a matrix argument","score":0.1982678472995758},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15096908807754517},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07201430201530457}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7370688915252686},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.6640490293502808},{"id":"https://openalex.org/C186348414","wikidata":"https://www.wikidata.org/wiki/Q526221","display_name":"Gauss sum","level":2,"score":0.6061676740646362},{"id":"https://openalex.org/C92941272","wikidata":"https://www.wikidata.org/wiki/Q1062958","display_name":"Basic hypergeometric series","level":3,"score":0.5901936888694763},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5821261405944824},{"id":"https://openalex.org/C15341905","wikidata":"https://www.wikidata.org/wiki/Q2164293","display_name":"Telescoping series","level":2,"score":0.5816873908042908},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.5444056987762451},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4866841435432434},{"id":"https://openalex.org/C60400383","wikidata":"https://www.wikidata.org/wiki/Q17028407","display_name":"Hypergeometric identity","level":5,"score":0.45819908380508423},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45138129591941833},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.44782885909080505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4400918185710907},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3926185965538025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.366299033164978},{"id":"https://openalex.org/C158241908","wikidata":"https://www.wikidata.org/wiki/Q109744257","display_name":"Generalized hypergeometric function","level":3,"score":0.3313373327255249},{"id":"https://openalex.org/C165175332","wikidata":"https://www.wikidata.org/wiki/Q5958021","display_name":"Hypergeometric function of a matrix argument","level":4,"score":0.1982678472995758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15096908807754517},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07201430201530457},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1394042.1394052","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1394042.1394052","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4223493164","https://openalex.org/W2988588764","https://openalex.org/W4297211345","https://openalex.org/W2080918621","https://openalex.org/W216983822","https://openalex.org/W2141941567","https://openalex.org/W4308347909","https://openalex.org/W3160935812","https://openalex.org/W2997609559","https://openalex.org/W2090364349"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,31],"q-WZ":[3],"method":[4],"for":[5],"justifying":[6],"nonterminating":[7],"basic":[8],"hypergeometric":[9],"summation":[10,36],"formulas":[11],"by":[12,72,111],"computing":[13],"the":[14,42,45,48,51,65,73,89,97,100,112],"WZ-pairs":[15],"as":[16],"certificates":[17],"which":[18],"may":[19],"involve":[20],"some":[21],"infinite":[22,113],"q-shifted":[23,114],"factorials.":[24,115],"Using":[25],"this":[26],"approach,":[27],"we":[28,62],"can":[29,63],"verify":[30],"wide":[32],"variety":[33],"of":[34,75],"classical":[35],"formulas,":[37],"with":[38,107],"typical":[39],"examples":[40],"including":[41],"q-binomial":[43],"theorem,":[44],"q-Gauss":[46],"sum,":[47,50,54],"6\u03c85":[49],"Ramanujan":[52],"1\u03c81":[53],"and":[55,86],"Bailey's":[56],"6\u03c86":[57],"sum.":[58],"In":[59],"many":[60],"cases":[61],"discover":[64],"companion":[66],"identities.":[67],"This":[68],"work":[69],"is":[70,103],"inspired":[71],"study":[74],"two":[76],"elegant":[77],"identities":[78],"involving":[79],"partial":[80],"theta":[81],"functions":[82],"due":[83],"to":[84,105],"Andrews":[85],"Warnaar":[87],"from":[88],"telescoping":[90],"viewpoint.":[91],"The":[92],"key":[93],"point":[94],"lies":[95],"in":[96],"fact":[98],"that":[99],"q-Gosper":[101],"algorithm":[102],"effective":[104],"deal":[106],"q-hypergeometric":[108],"terms":[109],"multiplied":[110]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}