{"id":"https://openalex.org/W1980348656","doi":"https://doi.org/10.1155/s016117120430743x","title":"Fourier transform and distributional representation of the gamma function leading to some new identities","display_name":"Fourier transform and distributional representation of the gamma function leading to some new identities","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1980348656","doi":"https://doi.org/10.1155/s016117120430743x","mag":"1980348656"},"language":"en","primary_location":{"id":"doi:10.1155/s016117120430743x","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s016117120430743x","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/S016117120430743X","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/S016117120430743X","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020833115","display_name":"M. A. Chaudhry","orcid":"https://orcid.org/0000-0002-6744-8841"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"M. Aslam Chaudhry","raw_affiliation_strings":["Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia, kfupm.edu.sa","Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia, kfupm.edu.sa","institution_ids":["https://openalex.org/I134085113"]},{"raw_affiliation_string":"Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078820796","display_name":"Asghar Qadir","orcid":"https://orcid.org/0000-0001-7114-2469"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]},{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK","SA"],"is_corresponding":false,"raw_author_name":"Asghar Qadir","raw_affiliation_strings":["Centre for Advanced Mathematics and Physics National University of Sciences and Technology Rawalpindi, Pakistan, nust.edu.pk","Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia, kfupm.edu.sa","Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Pakistan","Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Advanced Mathematics and Physics National University of Sciences and Technology Rawalpindi, Pakistan, nust.edu.pk","institution_ids":["https://openalex.org/I929597975"]},{"raw_affiliation_string":"Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia, kfupm.edu.sa","institution_ids":["https://openalex.org/I134085113"]},{"raw_affiliation_string":"Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Pakistan","institution_ids":["https://openalex.org/I929597975"]},{"raw_affiliation_string":"Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.4429,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.56014609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2004","issue":"39","first_page":"2091","last_page":"2096"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9937999844551086,"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":0.9937999844551086,"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":0.9861000180244446,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9783999919891357,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.7922669649124146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7885968685150146},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6831296682357788},{"id":"https://openalex.org/keywords/gamma-function","display_name":"Gamma function","score":0.5690048336982727},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5239712595939636},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45256713032722473},{"id":"https://openalex.org/keywords/function-representation","display_name":"Function representation","score":0.44006597995758057},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38279712200164795},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3745730519294739},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21622124314308167}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.7922669649124146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7885968685150146},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6831296682357788},{"id":"https://openalex.org/C82240120","wikidata":"https://www.wikidata.org/wiki/Q190573","display_name":"Gamma function","level":2,"score":0.5690048336982727},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5239712595939636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45256713032722473},{"id":"https://openalex.org/C167528306","wikidata":"https://www.wikidata.org/wiki/Q5508776","display_name":"Function representation","level":3,"score":0.44006597995758057},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38279712200164795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3745730519294739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21622124314308167},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/s016117120430743x","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s016117120430743x","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/S016117120430743X","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:912542","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2004/912542.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:0a929f128a584367a7e649bf81462521","is_oa":true,"landing_page_url":"https://doaj.org/article/0a929f128a584367a7e649bf81462521","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 39, Pp 2091-2096 (2004)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/S016117120430743X","is_oa":false,"landing_page_url":"https://doi.org/10.1155/S016117120430743X","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1155/s016117120430743x","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s016117120430743x","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/S016117120430743X","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322323","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1980348656.pdf","grobid_xml":"https://content.openalex.org/works/W1980348656.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W634226594","https://openalex.org/W1485979810","https://openalex.org/W1489991626","https://openalex.org/W3202780401","https://openalex.org/W4230941884","https://openalex.org/W4292095448"],"related_works":["https://openalex.org/W2062195135","https://openalex.org/W2795079307","https://openalex.org/W2793058541","https://openalex.org/W2748095760","https://openalex.org/W784984900","https://openalex.org/W2088334249","https://openalex.org/W2020444791","https://openalex.org/W1521729451","https://openalex.org/W3171252057","https://openalex.org/W1980348656"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,14],"Fourier":[3],"transform":[4],"representation":[5,16],"of":[6,20,30],"the":[7,28],"gamma":[8,31],"functions,":[9,36],"which":[10,37],"leads":[11],"naturally":[12],"to":[13,24],"distributional":[15],"for":[17,27],"them.":[18],"Both":[19],"these":[21],"representations":[22],"lead":[23],"new":[25],"identities":[26],"integrals":[29],"functions":[32],"multiplied":[33],"by":[34],"other":[35],"are":[38],"also":[39],"presented":[40],"here.":[41]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}