{"id":"https://openalex.org/W2035158677","doi":"https://doi.org/10.1080/00207160701242326","title":"A note on generalized Euler numbers and polynomials","display_name":"A note on generalized Euler numbers and polynomials","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2035158677","doi":"https://doi.org/10.1080/00207160701242326","mag":"2035158677"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701242326","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701242326","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/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":"C. S. Ryoo","raw_affiliation_strings":["a   Department of Mathematics , Hannam University , Daejeon, 306-791,  Korea","Department of Mathematics , Hannam University , Daejeon, 306-791, Korea"],"affiliations":[{"raw_affiliation_string":"a   Department of Mathematics , Hannam University , Daejeon, 306-791,  Korea","institution_ids":["https://openalex.org/I112728665"]},{"raw_affiliation_string":"Department of Mathematics , Hannam University , Daejeon, 306-791, Korea","institution_ids":["https://openalex.org/I112728665"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039903601","display_name":"T. Kim","orcid":"https://orcid.org/0009-0003-5047-7501"},"institutions":[{"id":"https://openalex.org/I31419693","display_name":"Kyungpook National University","ror":"https://ror.org/040c17130","country_code":"KR","type":"education","lineage":["https://openalex.org/I31419693"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"T. Kim","raw_affiliation_strings":["b   EECS , Kyungpook National University , Taegu, 702-701,  Korea","EECS , Kyungpook National University , Taegu, 702-701, Korea"],"affiliations":[{"raw_affiliation_string":"b   EECS , Kyungpook National University , Taegu, 702-701,  Korea","institution_ids":["https://openalex.org/I31419693"]},{"raw_affiliation_string":"EECS , Kyungpook National University , Taegu, 702-701, Korea","institution_ids":["https://openalex.org/I31419693"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049662161","display_name":"Lee-Chae Jang","orcid":"https://orcid.org/0000-0001-5317-1725"},"institutions":[{"id":"https://openalex.org/I24062138","display_name":"Konkuk University","ror":"https://ror.org/025h1m602","country_code":"KR","type":"education","lineage":["https://openalex.org/I24062138"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"L. C. Jang","raw_affiliation_strings":["c   Department of Mathematics and Computer Science , KonKuk University , Choongju, 380-701,  Korea","Department of Mathematics and Computer Science , KonKuk University , Choongju, 380-701, Korea"],"affiliations":[{"raw_affiliation_string":"c   Department of Mathematics and Computer Science , KonKuk University , Choongju, 380-701,  Korea","institution_ids":["https://openalex.org/I24062138"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science , KonKuk University , Choongju, 380-701, Korea","institution_ids":["https://openalex.org/I24062138"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111969523"],"corresponding_institution_ids":["https://openalex.org/I112728665"],"apc_list":null,"apc_paid":null,"fwci":1.6272,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80836941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"84","issue":"7","first_page":"1099","last_page":"1111"},"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":0.9976999759674072,"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":0.9955000281333923,"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/mathematics","display_name":"Mathematics","score":0.8750815391540527},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.7205754518508911},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.5331627130508423},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.5204165577888489},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.5115326642990112},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.5112853050231934},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.49268561601638794},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4686671495437622},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.46050259470939636},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4579521417617798},{"id":"https://openalex.org/keywords/euler-summation","display_name":"Euler summation","score":0.42449212074279785},{"id":"https://openalex.org/keywords/euler-number","display_name":"Euler number (physics)","score":0.41117531061172485},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.34476009011268616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2775641977787018},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.20279422402381897},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.05983087420463562},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.047557979822158813}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8750815391540527},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.7205754518508911},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.5331627130508423},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.5204165577888489},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.5115326642990112},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.5112853050231934},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.49268561601638794},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4686671495437622},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.46050259470939636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4579521417617798},{"id":"https://openalex.org/C48330753","wikidata":"https://www.wikidata.org/wiki/Q374926","display_name":"Euler summation","level":5,"score":0.42449212074279785},{"id":"https://openalex.org/C196102512","wikidata":"https://www.wikidata.org/wiki/Q1340031","display_name":"Euler number (physics)","level":5,"score":0.41117531061172485},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.34476009011268616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2775641977787018},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.20279422402381897},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.05983087420463562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.047557979822158813},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701242326","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701242326","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321229","display_name":"Hannam University","ror":"https://ror.org/01cwbae71"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1560534892","https://openalex.org/W1971393827","https://openalex.org/W1983902089","https://openalex.org/W1991213313","https://openalex.org/W2000534764","https://openalex.org/W2020157504","https://openalex.org/W2039850961","https://openalex.org/W2056668637","https://openalex.org/W2063754977","https://openalex.org/W2081325706","https://openalex.org/W2094553193","https://openalex.org/W2107195277","https://openalex.org/W2116922032","https://openalex.org/W2125357087","https://openalex.org/W2322634390","https://openalex.org/W2962976658","https://openalex.org/W3204546449","https://openalex.org/W3207970702","https://openalex.org/W4231558066","https://openalex.org/W4244058206"],"related_works":["https://openalex.org/W2349703342","https://openalex.org/W92860307","https://openalex.org/W1555875796","https://openalex.org/W1993878402","https://openalex.org/W1544888911","https://openalex.org/W2037587809","https://openalex.org/W2941483924","https://openalex.org/W2353944719","https://openalex.org/W2746651491","https://openalex.org/W2606829290"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,48],"construct":[4],"new":[5],"generalized":[6,10,26,41,55],"Euler":[7,11,27,42,56],"polynomials":[8,43,57],"and":[9],"numbers":[12],"attached":[13],"to":[14,25],"\u03c7.":[15],"We":[16,29],"investigate":[17,49],"some":[18],"of":[19,34,53,63],"the":[20,32,51,54,64],"properties":[21],"that":[22,39],"are":[23],"related":[24],"polynomials.":[28],"also":[30],"derive":[31],"existence":[33],"a":[35],"specific":[36],"interpolation":[37],"function":[38],"interpolates":[40],"at":[44],"negative":[45],"integers.":[46],"Finally,":[47],"computationally":[50],"roots":[52],"E":[58],"n,":[59],"\u03c7(x)":[60],"for":[61],"values":[62],"index":[65],"n.":[66]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
