{"id":"https://openalex.org/W7142016276","doi":"https://doi.org/10.1002/mma.70700","title":"Novel Generating Functions Related to Gaussian Numbers and Its Applications for Modeling the Harmonic Oscillators","display_name":"Novel Generating Functions Related to Gaussian Numbers and Its Applications for Modeling the Harmonic Oscillators","publication_year":2026,"publication_date":"2026-03-27","ids":{"openalex":"https://openalex.org/W7142016276","doi":"https://doi.org/10.1002/mma.70700"},"language":"en","primary_location":{"id":"doi:10.1002/mma.70700","doi":"https://doi.org/10.1002/mma.70700","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mma.70700","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"},"volume":null,"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/A5130859536","display_name":"Dounya Hamek","orcid":"https://orcid.org/0009-0001-7247-2950","observed_orcids":["https://orcid.org/0009-0001-7247-2950"]},"institutions":[{"id":"https://openalex.org/I116970179","display_name":"University of Jijel","ror":"https://ror.org/03kkfk814","country_code":"DZ","type":"education","lineage":["https://openalex.org/I116970179"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Dounya Hamek","raw_affiliation_strings":["LMEPA Laboratory Materials Mohamed Seddik Ben Yahia University  Jijel Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMEPA Laboratory Materials Mohamed Seddik Ben Yahia University  Jijel Algeria","institution_ids":["https://openalex.org/I116970179"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007834454","display_name":"Ali Boussayoud","orcid":"https://orcid.org/0000-0001-5553-3240","observed_orcids":["https://orcid.org/0000-0001-5553-3240"]},"institutions":[{"id":"https://openalex.org/I116970179","display_name":"University of Jijel","ror":"https://ror.org/03kkfk814","country_code":"DZ","type":"education","lineage":["https://openalex.org/I116970179"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Ali Boussayoud","raw_affiliation_strings":["Faculty of Exact Sciences and Informatics, LMAM Laboratory and Department of Mathematics Mohamed Seddik Ben Yahia University  Jijel Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Exact Sciences and Informatics, LMAM Laboratory and Department of Mathematics Mohamed Seddik Ben Yahia University  Jijel Algeria","institution_ids":["https://openalex.org/I116970179"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071351787","display_name":"Salah Boulaaras","orcid":"https://orcid.org/0000-0003-1308-2159","observed_orcids":["https://orcid.org/0000-0003-1308-2159"]},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Salah Boulaaras","raw_affiliation_strings":["Department of Mathematics, College of Science Qassim University  Buraydah Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1308-2159","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science Qassim University  Buraydah Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068914562","display_name":"Chems Eddine Arroud","orcid":"https://orcid.org/0000-0002-1688-5160","observed_orcids":["https://orcid.org/0000-0002-1688-5160"]},"institutions":[{"id":"https://openalex.org/I116970179","display_name":"University of Jijel","ror":"https://ror.org/03kkfk814","country_code":"DZ","type":"education","lineage":["https://openalex.org/I116970179"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Chems Eddine Arroud","raw_affiliation_strings":["Faculty of Exact Sciences and Informatics, Department of Mathematics Mohamed Seddik Ben Yahia University  Jijel Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Exact Sciences and Informatics, Department of Mathematics Mohamed Seddik Ben Yahia University  Jijel Algeria","institution_ids":["https://openalex.org/I116970179"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049447473","display_name":"Nesrine Harrouche","orcid":"https://orcid.org/0009-0002-4697-5885","observed_orcids":["https://orcid.org/0009-0002-4697-5885"]},"institutions":[{"id":"https://openalex.org/I116970179","display_name":"University of Jijel","ror":"https://ror.org/03kkfk814","country_code":"DZ","type":"education","lineage":["https://openalex.org/I116970179"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Nesrine Harrouche","raw_affiliation_strings":["Faculty of Exact Sciences and Informatics, Department of Mathematics Mohamed Seddik Ben Yahia University  Jijel Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Exact Sciences and Informatics, Department of Mathematics Mohamed Seddik Ben Yahia University  Jijel Algeria","institution_ids":["https://openalex.org/I116970179"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024995057","display_name":"Baghdadi Aloui","orcid":"https://orcid.org/0000-0003-2493-6615","observed_orcids":["https://orcid.org/0000-0003-2493-6615"]},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]},{"id":"https://openalex.org/I4405252705","display_name":"Faculty of Sciences of Sfax","ror":"https://ror.org/01thp0k37","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784","https://openalex.org/I4405252705"]},{"id":"https://openalex.org/I68916915","display_name":"University of Gab\u00e8s","ror":"https://ror.org/022efad20","country_code":"TN","type":"education","lineage":["https://openalex.org/I68916915"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Baghdadi Aloui","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences of Sfax Sfax University  Sfax Tunisia","Research Laboratory of Mathematics and Applications LR17ES11 Gabes University  Gabes Tunisia"],"raw_orcid":"https://orcid.org/0000-0003-2493-6615","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences of Sfax Sfax University  Sfax Tunisia","institution_ids":["https://openalex.org/I142899784","https://openalex.org/I4405252705"]},{"raw_affiliation_string":"Research Laboratory of Mathematics and Applications LR17ES11 Gabes University  Gabes Tunisia","institution_ids":["https://openalex.org/I68916915"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5024995057"],"corresponding_institution_ids":["https://openalex.org/I142899784","https://openalex.org/I4405252705","https://openalex.org/I68916915"],"apc_list":{"value":5000,"currency":"USD","value_usd":5000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22843646,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"11","first_page":"12539","last_page":"12564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.8521000146865845,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.8521000146865845,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.10909999907016754,"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":0.03150000050663948,"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/generating-functions","display_name":"generating functions","score":0.9800000190734863},{"id":"https://openalex.org/keywords/complex-numbers","display_name":"complex numbers","score":0.47600001096725464},{"id":"https://openalex.org/keywords/symmetric-functions","display_name":"symmetric functions","score":0.8479999899864197},{"id":"https://openalex.org/keywords/bivariate-polynomials","display_name":"bivariate polynomials","score":0.8870000243186951},{"id":"https://openalex.org/keywords/quantum-harmonic-oscillator","display_name":"quantum harmonic oscillator","score":0.7639999985694885},{"id":"https://openalex.org/keywords/complex-interactions","display_name":"complex interactions","score":0.7699999809265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8565000295639038},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6395999789237976},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6334999799728394},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5252000093460083},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.49410000443458557},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.44209998846054077},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4359000027179718},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3790000081062317},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.3571999967098236},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3379000127315521},{"id":"https://openalex.org/C122332657","wikidata":"https://www.wikidata.org/wiki/Q677864","display_name":"Quantum harmonic oscillator","level":3,"score":0.32190001010894775},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29789999127388},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2962999939918518},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C187825244","wikidata":"https://www.wikidata.org/wiki/Q372071","display_name":"Probability-generating function","level":4,"score":0.25290000438690186},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/mma.70700","doi":"https://doi.org/10.1002/mma.70700","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mma.70700","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1993225914","https://openalex.org/W2054893952","https://openalex.org/W2923054028","https://openalex.org/W2955372169","https://openalex.org/W3107504695","https://openalex.org/W3129164548","https://openalex.org/W3152443824","https://openalex.org/W3194004528","https://openalex.org/W4382488259"],"related_works":[],"abstract_inverted_index":{"ABSTRACT":[0],"In":[1],"this":[2],"study,":[3],"through":[4],"the":[5,23,45],"utilization":[6],"of":[7,22,25],"properties":[8],"associated":[9],"with":[10,28,48],"symmetric":[11],"functions,":[12],"we":[13,38],"establish":[14],"a":[15],"novel":[16],"theorem":[17],"and":[18,32],"develop":[19],"generating":[20,41],"functions":[21,42],"products":[24],"Gaussian":[26],"numbers":[27],"numbers,":[29],"bivariate":[30],"polynomials":[31],"certain":[33],"polynomials.":[34],"As":[35],"an":[36],"application,":[37],"use":[39],"these":[40],"for":[43],"modeling":[44],"quantum":[46],"oscillators":[47],"complex":[49],"interactions.":[50]},"counts_by_year":[],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2026-03-29T00:00:00"}
