{"id":"https://openalex.org/W4399974831","doi":"https://doi.org/10.3390/axioms13070421","title":"Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on \u2124p","display_name":"Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on \u2124p","publication_year":2024,"publication_date":"2024-06-22","ids":{"openalex":"https://openalex.org/W4399974831","doi":"https://doi.org/10.3390/axioms13070421"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13070421","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070421","pdf_url":"https://www.mdpi.com/2075-1680/13/7/421/pdf?version=1719046718","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/7/421/pdf?version=1719046718","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046233988","display_name":"Maryam Salem Alatawi","orcid":"https://orcid.org/0000-0002-5567-7444"},"institutions":[{"id":"https://openalex.org/I72264486","display_name":"University of Tabuk","ror":"https://ror.org/04yej8x59","country_code":"SA","type":"education","lineage":["https://openalex.org/I72264486"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Maryam Salem Alatawi","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5567-7444","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia","institution_ids":["https://openalex.org/I72264486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067814181","display_name":"Waseem Ahmad Khan","orcid":"https://orcid.org/0000-0002-4681-9885"},"institutions":[{"id":"https://openalex.org/I138564716","display_name":"Prince Mohammad bin Fahd University","ror":"https://ror.org/03d64na34","country_code":"SA","type":"education","lineage":["https://openalex.org/I138564716"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Waseem Ahmad Khan","raw_affiliation_strings":["Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-4681-9885","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia","institution_ids":["https://openalex.org/I138564716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061752199","display_name":"U\u011fur Duran","orcid":"https://orcid.org/0000-0002-5717-1199"},"institutions":[{"id":"https://openalex.org/I4210155859","display_name":"\u0130skenderun Technical University","ror":"https://ror.org/052nzqz14","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210155859"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ugur Duran","raw_affiliation_strings":["Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay 31200, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-5717-1199","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay 31200, T\u00fcrkiye","institution_ids":["https://openalex.org/I4210155859"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067814181"],"corresponding_institution_ids":["https://openalex.org/I138564716"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.5237,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.92708138,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"13","issue":"7","first_page":"421","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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":0.9998999834060669,"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":0.996399998664856,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7667367458343506},{"id":"https://openalex.org/keywords/fubinis-theorem","display_name":"Fubini's theorem","score":0.6934520602226257},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6594272255897522},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5573326945304871},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.49369511008262634},{"id":"https://openalex.org/keywords/koornwinder-polynomials","display_name":"Koornwinder polynomials","score":0.4691672921180725},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4590209424495697},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.4485793709754944},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.3956526219844818},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34326261281967163},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09935504198074341},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09747475385665894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7667367458343506},{"id":"https://openalex.org/C55526981","wikidata":"https://www.wikidata.org/wiki/Q1149022","display_name":"Fubini's theorem","level":2,"score":0.6934520602226257},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6594272255897522},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5573326945304871},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.49369511008262634},{"id":"https://openalex.org/C5056958","wikidata":"https://www.wikidata.org/wiki/Q6430769","display_name":"Koornwinder polynomials","level":5,"score":0.4691672921180725},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4590209424495697},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.4485793709754944},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.3956526219844818},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34326261281967163},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09935504198074341},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09747475385665894}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13070421","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070421","pdf_url":"https://www.mdpi.com/2075-1680/13/7/421/pdf?version=1719046718","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1d70297bb2434c589734b409cf7b5f73","is_oa":true,"landing_page_url":"https://doaj.org/article/1d70297bb2434c589734b409cf7b5f73","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":"Axioms, Vol 13, Iss 7, p 421 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13070421","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070421","pdf_url":"https://www.mdpi.com/2075-1680/13/7/421/pdf?version=1719046718","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4399974831.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1994303451","https://openalex.org/W2020157504","https://openalex.org/W2102355088","https://openalex.org/W2154938900","https://openalex.org/W2164304403","https://openalex.org/W2746903834","https://openalex.org/W2894000865","https://openalex.org/W2912860995","https://openalex.org/W2940473210","https://openalex.org/W2946844585","https://openalex.org/W2952324985","https://openalex.org/W2960490941","https://openalex.org/W2991659901","https://openalex.org/W3012284275","https://openalex.org/W3028483956","https://openalex.org/W3028837265","https://openalex.org/W3092984393","https://openalex.org/W3160181372","https://openalex.org/W3162454302","https://openalex.org/W3171714738","https://openalex.org/W3213582390","https://openalex.org/W4224929693","https://openalex.org/W6743542937","https://openalex.org/W6778169702","https://openalex.org/W6794701058","https://openalex.org/W6795120251","https://openalex.org/W6803956875","https://openalex.org/W7024856691"],"related_works":["https://openalex.org/W2132314122","https://openalex.org/W2510621088","https://openalex.org/W1549388788","https://openalex.org/W2051848833","https://openalex.org/W2168893271","https://openalex.org/W2078527818","https://openalex.org/W2070537393","https://openalex.org/W4380152001","https://openalex.org/W4322760296","https://openalex.org/W1825644555"],"abstract_inverted_index":{"Since":[0],"the":[1,57,66,143,157,162,172,178],"constructions":[2],"of":[3,21,35,38,56,60,69,82,99,112,140,156,177],"p-adic":[4,109,128],"q-integrals,":[5],"these":[6,61,113,124],"integrals":[7,62],"as":[8,10,18,44],"well":[9],"particular":[11],"cases":[12],"have":[13],"been":[14],"used":[15],"not":[16],"only":[17],"integral":[19,110,129],"representations":[20],"many":[22,36],"special":[23,39,71,127],"functions,":[24],"polynomials,":[25,42],"and":[26,41,50,53],"numbers,":[27],"but":[28],"they":[29],"also":[30],"allow":[31],"for":[32,64,123,142],"deep":[33],"examinations":[34],"families":[37],"numbers":[40,52],"such":[43],"central":[45,48,84,94,148,167,174],"Fubini,":[46],"Bernoulli,":[47],"Bell,":[49],"Changhee":[51],"polynomials.":[54,72,86,114,150],"One":[55],"key":[58],"applications":[59],"is":[63],"obtaining":[65],"symmetric":[67,121],"identities":[68,122],"certain":[70],"In":[73],"this":[74,116],"study,":[75],"we":[76,88,105,118,136,152],"focus":[77],"on":[78,161],"a":[79,107,154],"novel":[80],"generalization":[81],"degenerate":[83,92,146,158,165,173],"Fubini":[85,95,149,168],"First,":[87],"introduce":[89],"two":[90,144,163],"variable":[91,145,164],"w-torsion":[93,147,166],"polynomials":[96,125,169,176],"by":[97],"means":[98],"their":[100],"exponential":[101],"generating":[102],"function.":[103],"Then,":[104],"provide":[106,153],"fermionic":[108],"representation":[111,155],"Through":[115],"representation,":[117],"investigate":[119],"several":[120],"using":[126,132],"techniques.":[130],"Also,":[131],"series":[133],"manipulation":[134],"methods,":[135],"obtain":[137],"an":[138],"identity":[139],"symmetry":[141],"Finally,":[151],"differential":[159],"operator":[160],"related":[170],"to":[171],"factorial":[175],"second":[179],"kind.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
