{"id":"https://openalex.org/W3205957286","doi":"https://doi.org/10.3390/axioms10040261","title":"Some Unified Integrals for Generalized Mittag-Leffler Functions","display_name":"Some Unified Integrals for Generalized Mittag-Leffler Functions","publication_year":2021,"publication_date":"2021-10-19","ids":{"openalex":"https://openalex.org/W3205957286","doi":"https://doi.org/10.3390/axioms10040261","mag":"3205957286"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10040261","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040261","pdf_url":"https://www.mdpi.com/2075-1680/10/4/261/pdf?version=1634705146","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/2075-1680/10/4/261/pdf?version=1634705146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001189006","display_name":"Prakash Singh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210126659","display_name":"Poornima University","ror":"https://ror.org/03gnqp653","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210126659"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Prakash Singh","raw_affiliation_strings":["Department of Mathematics, Research Scholar, Poornima University, Jaipur 303905, India"],"raw_orcid":"https://orcid.org/0000-0002-6960-9338","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Research Scholar, Poornima University, Jaipur 303905, India","institution_ids":["https://openalex.org/I4210126659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107875950","display_name":"Shilpi Jain","orcid":"https://orcid.org/0000-0002-0906-2801"},"institutions":[{"id":"https://openalex.org/I4210126659","display_name":"Poornima University","ror":"https://ror.org/03gnqp653","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210126659"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shilpi Jain","raw_affiliation_strings":["Department of Mathematics, Poornima University, Jaipur 303905, India"],"raw_orcid":"https://orcid.org/0000-0002-0906-2801","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Poornima University, Jaipur 303905, India","institution_ids":["https://openalex.org/I4210126659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022405104","display_name":"Carlo Cattani","orcid":"https://orcid.org/0000-0002-7504-0424"},"institutions":[{"id":"https://openalex.org/I138938424","display_name":"Universit\u00e0 degli Studi della Tuscia","ror":"https://ror.org/03svwq685","country_code":"IT","type":"education","lineage":["https://openalex.org/I138938424"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Carlo Cattani","raw_affiliation_strings":["Engineering School (DEIM), University of Tuscia, 01100 Viterbo, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7504-0424","affiliations":[{"raw_affiliation_string":"Engineering School (DEIM), University of Tuscia, 01100 Viterbo, Italy","institution_ids":["https://openalex.org/I138938424"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022405104"],"corresponding_institution_ids":["https://openalex.org/I138938424"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":1.2781,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78757903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"10","issue":"4","first_page":"261","last_page":"261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9995999932289124,"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":0.9995999932289124,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/generalized-hypergeometric-function","display_name":"Generalized hypergeometric function","score":0.7635189294815063},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.7229350209236145},{"id":"https://openalex.org/keywords/barnes-integral","display_name":"Barnes integral","score":0.7091113924980164},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7058184742927551},{"id":"https://openalex.org/keywords/generalized-function","display_name":"Generalized function","score":0.564530611038208},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5566076636314392},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5173577666282654},{"id":"https://openalex.org/keywords/special-functions","display_name":"Special functions","score":0.5163809061050415},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5055065155029297},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5046554803848267},{"id":"https://openalex.org/keywords/elementary-function","display_name":"Elementary function","score":0.4562455713748932},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4476607143878937},{"id":"https://openalex.org/keywords/wright","display_name":"Wright","score":0.4381502866744995},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.347989022731781},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32180625200271606},{"id":"https://openalex.org/keywords/hypergeometric-function-of-a-matrix-argument","display_name":"Hypergeometric function of a matrix argument","score":0.2939399778842926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11451977491378784}],"concepts":[{"id":"https://openalex.org/C158241908","wikidata":"https://www.wikidata.org/wiki/Q109744257","display_name":"Generalized hypergeometric function","level":3,"score":0.7635189294815063},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.7229350209236145},{"id":"https://openalex.org/C148421525","wikidata":"https://www.wikidata.org/wiki/Q4201931","display_name":"Barnes integral","level":5,"score":0.7091113924980164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7058184742927551},{"id":"https://openalex.org/C69151251","wikidata":"https://www.wikidata.org/wiki/Q846537","display_name":"Generalized function","level":2,"score":0.564530611038208},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5566076636314392},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5173577666282654},{"id":"https://openalex.org/C50757856","wikidata":"https://www.wikidata.org/wiki/Q867707","display_name":"Special functions","level":2,"score":0.5163809061050415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5055065155029297},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5046554803848267},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.4562455713748932},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4476607143878937},{"id":"https://openalex.org/C2777667586","wikidata":"https://www.wikidata.org/wiki/Q8038170","display_name":"Wright","level":2,"score":0.4381502866744995},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.347989022731781},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32180625200271606},{"id":"https://openalex.org/C165175332","wikidata":"https://www.wikidata.org/wiki/Q5958021","display_name":"Hypergeometric function of a matrix argument","level":4,"score":0.2939399778842926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11451977491378784},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms10040261","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040261","pdf_url":"https://www.mdpi.com/2075-1680/10/4/261/pdf?version=1634705146","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:22c5e38f07fc412b8712bcb6f84e300f","is_oa":true,"landing_page_url":"https://doaj.org/article/22c5e38f07fc412b8712bcb6f84e300f","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 10, Iss 4, p 261 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/4/261/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10040261","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 10; Issue 4; Pages: 261","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms10040261","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040261","pdf_url":"https://www.mdpi.com/2075-1680/10/4/261/pdf?version=1634705146","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3205957286.pdf","grobid_xml":"https://content.openalex.org/works/W3205957286.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W68100126","https://openalex.org/W69681244","https://openalex.org/W126395531","https://openalex.org/W1570034505","https://openalex.org/W1991202559","https://openalex.org/W2008295296","https://openalex.org/W2038650800","https://openalex.org/W2071031363","https://openalex.org/W2134928079","https://openalex.org/W2190750553","https://openalex.org/W2500436220","https://openalex.org/W2797385772","https://openalex.org/W2883179813","https://openalex.org/W3031197895","https://openalex.org/W3158648665","https://openalex.org/W3194159241","https://openalex.org/W6602848315","https://openalex.org/W6605185477","https://openalex.org/W6667912487","https://openalex.org/W6750167019","https://openalex.org/W6753160426"],"related_works":["https://openalex.org/W3098293399","https://openalex.org/W2997127250","https://openalex.org/W2047062626","https://openalex.org/W3115897507","https://openalex.org/W4385548942","https://openalex.org/W4288019568","https://openalex.org/W2018821987","https://openalex.org/W3205957286","https://openalex.org/W2487195786","https://openalex.org/W2031273182"],"abstract_inverted_index":{"Here,":[0],"we":[1],"ascertain":[2],"generalized":[3,11,24],"integral":[4,15],"formulas":[5,16],"concerning":[6],"the":[7,10,20,23,36],"product":[8],"of":[9,22,35],"Mittag-Leffler":[12],"function.":[13,39],"These":[14],"are":[17,30],"described":[18],"in":[19,33],"form":[21],"Lauricella":[25],"series.":[26],"Some":[27],"special":[28],"cases":[29],"also":[31],"presented":[32],"terms":[34],"Wright":[37],"hypergeometric":[38]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
