{"id":"https://openalex.org/W2944743666","doi":"https://doi.org/10.3390/sym11050645","title":"Some Symmetric Identities for the Multiple (p, q)-Hurwitz-Euler eta Function","display_name":"Some Symmetric Identities for the Multiple (p, q)-Hurwitz-Euler eta Function","publication_year":2019,"publication_date":"2019-05-08","ids":{"openalex":"https://openalex.org/W2944743666","doi":"https://doi.org/10.3390/sym11050645","mag":"2944743666"},"language":"en","primary_location":{"id":"doi:10.3390/sym11050645","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11050645","pdf_url":"https://www.mdpi.com/2073-8994/11/5/645/pdf?version=1557298888","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/5/645/pdf?version=1557298888","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004869352","display_name":"Kyung-Won Hwang","orcid":"https://orcid.org/0000-0001-7000-2325"},"institutions":[{"id":"https://openalex.org/I51226738","display_name":"Dong-A University","ror":"https://ror.org/03qvtpc38","country_code":"KR","type":"education","lineage":["https://openalex.org/I51226738"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kyung-Won Hwang","raw_affiliation_strings":["Department of Mathematics, Dong-A University, Busan 604-714, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dong-A University, Busan 604-714, Korea","institution_ids":["https://openalex.org/I51226738"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111969523","display_name":"C. S. Ryoo","orcid":null},"institutions":[{"id":"https://openalex.org/I112728665","display_name":"Hannam University","ror":"https://ror.org/01cwbae71","country_code":"KR","type":"education","lineage":["https://openalex.org/I112728665"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Cheon Seoung Ryoo","raw_affiliation_strings":["Department of Mathematics, Hannam University, Daejeon 34430, Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hannam University, Daejeon 34430, Korea","institution_ids":["https://openalex.org/I112728665"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111969523"],"corresponding_institution_ids":["https://openalex.org/I112728665"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9194,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84758286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"5","first_page":"645","last_page":"645"},"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":0.9976000189781189,"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":0.9944000244140625,"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/eulers-formula","display_name":"Euler's formula","score":0.7410861253738403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7234117388725281},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6317362785339355},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5483341217041016},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5120154023170471},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4860542118549347},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4736170470714569},{"id":"https://openalex.org/keywords/ring-of-symmetric-functions","display_name":"Ring of symmetric functions","score":0.4606075584888458},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4383425712585449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4373306334018707},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.40080526471138},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.2716670334339142},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2169448733329773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0485861599445343}],"concepts":[{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.7410861253738403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7234117388725281},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6317362785339355},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5483341217041016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5120154023170471},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4860542118549347},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4736170470714569},{"id":"https://openalex.org/C156903151","wikidata":"https://www.wikidata.org/wiki/Q17102788","display_name":"Ring of symmetric functions","level":4,"score":0.4606075584888458},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4383425712585449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4373306334018707},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.40080526471138},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.2716670334339142},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2169448733329773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0485861599445343},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11050645","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11050645","pdf_url":"https://www.mdpi.com/2073-8994/11/5/645/pdf?version=1557298888","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3b01fad057544fdb9097c65b5c9c1570","is_oa":true,"landing_page_url":"https://doaj.org/article/3b01fad057544fdb9097c65b5c9c1570","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 5, p 645 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11050645","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11050645","pdf_url":"https://www.mdpi.com/2073-8994/11/5/645/pdf?version=1557298888","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2944743666.pdf","grobid_xml":"https://content.openalex.org/works/W2944743666.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1482634932","https://openalex.org/W1965454233","https://openalex.org/W1989480191","https://openalex.org/W1997598904","https://openalex.org/W2019149683","https://openalex.org/W2030391314","https://openalex.org/W2052705629","https://openalex.org/W2060489440","https://openalex.org/W2359969474","https://openalex.org/W2485900856","https://openalex.org/W2518437148","https://openalex.org/W2554855051","https://openalex.org/W2579972501","https://openalex.org/W2605564757","https://openalex.org/W3171357074","https://openalex.org/W4231062687","https://openalex.org/W6663451542","https://openalex.org/W6726356726","https://openalex.org/W6797284020","https://openalex.org/W6824805347"],"related_works":["https://openalex.org/W2893614166","https://openalex.org/W2003769335","https://openalex.org/W2081607056","https://openalex.org/W2761935536","https://openalex.org/W2035948520","https://openalex.org/W4385682000","https://openalex.org/W1966731002","https://openalex.org/W4313408517","https://openalex.org/W2964003717","https://openalex.org/W2063305861"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,132,135],"this":[4],"paper":[5],"is":[6],"to":[7],"find":[8,55,77],"some":[9,56],"interesting":[10],"symmetric":[11,79,94,130],"identities":[12,80,95],"for":[13,81,96],"the":[14,30,42,127,133],"(":[15,32,45,64,83,99,116,138],"p":[16,33,46,65,84,100,117,139],",":[17,34,47,66,85,101,118,140],"q":[18,35,48,67,86,102,119,141],")":[19,36,49,68,87,103,120,142],"-Hurwitz-Euler":[20,37,88,121],"eta":[21,38,89,122],"function":[22,39],"in":[23,61],"a":[24],"complex":[25],"field.":[26],"Firstly,":[27],"we":[28,125],"define":[29],"multiple":[31,82,115],"by":[40,111],"generalizing":[41],"Carlitz\u2019s":[43,62,97,136],"form":[44,63,98,137],"-Euler":[50,69,104,143],"numbers":[51,70,105,144],"and":[52,58,71,106,129,145],"polynomials.":[53],"We":[54,76,91],"formulas":[57],"properties":[59,131],"involved":[60],"polynomials":[72,107,146],"with":[73,108,147],"higher":[74,109,148],"order.":[75,149],"new":[78],"functions.":[90,123],"also":[92],"obtain":[93],"order":[110],"using":[112],"symmetry":[113],"about":[114],"Finally,":[124],"study":[126],"distribution":[128],"zero":[134]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-05-16T00:00:00"}
