{"id":"https://openalex.org/W4280636005","doi":"https://doi.org/10.3390/sym14051007","title":"Subordination Involving Regular Coulomb Wave Functions","display_name":"Subordination Involving Regular Coulomb Wave Functions","publication_year":2022,"publication_date":"2022-05-16","ids":{"openalex":"https://openalex.org/W4280636005","doi":"https://doi.org/10.3390/sym14051007"},"language":"en","primary_location":{"id":"doi:10.3390/sym14051007","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051007","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1007/pdf?version=1652681960","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/5/1007/pdf?version=1652681960","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005728762","display_name":"Saiful R. Mondal","orcid":"https://orcid.org/0000-0003-4540-1601"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Saiful R. Mondal","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Al Hasa 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4540-1601","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Al Hasa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005728762"],"corresponding_institution_ids":["https://openalex.org/I4626487"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9536,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85225225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"5","first_page":"1007","last_page":"1007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T14303","display_name":"Polymer Synthesis and Characterization","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/2507","display_name":"Polymers and Plastics"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10939","display_name":"Crystal Structures and Properties","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subordination","display_name":"Subordination (linguistics)","score":0.9220874309539795},{"id":"https://openalex.org/keywords/coulomb","display_name":"Coulomb","score":0.7977453470230103},{"id":"https://openalex.org/keywords/coulomb-wave-function","display_name":"Coulomb wave function","score":0.7403111457824707},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.5910115838050842},{"id":"https://openalex.org/keywords/wave-function","display_name":"Wave function","score":0.5819382667541504},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5527872443199158},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5011162757873535},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4718829393386841},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4546923041343689},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3856582045555115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3619700074195862},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.28974759578704834}],"concepts":[{"id":"https://openalex.org/C2777406531","wikidata":"https://www.wikidata.org/wiki/Q2031017","display_name":"Subordination (linguistics)","level":2,"score":0.9220874309539795},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.7977453470230103},{"id":"https://openalex.org/C14969097","wikidata":"https://www.wikidata.org/wiki/Q17007968","display_name":"Coulomb wave function","level":4,"score":0.7403111457824707},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.5910115838050842},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.5819382667541504},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5527872443199158},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5011162757873535},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4718829393386841},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4546923041343689},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3856582045555115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3619700074195862},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.28974759578704834},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14051007","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051007","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1007/pdf?version=1652681960","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1c6ef8ef2673422ab39b1ae2c6295d62","is_oa":true,"landing_page_url":"https://doaj.org/article/1c6ef8ef2673422ab39b1ae2c6295d62","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":"Symmetry, Vol 14, Iss 5, p 1007 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/1007/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14051007","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14051007","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051007","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1007/pdf?version=1652681960","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1489522182","display_name":null,"funder_award_id":"AN00097","funder_id":"https://openalex.org/F4320322804","funder_display_name":"Deanship of Scientific Research, King Faisal University"}],"funders":[{"id":"https://openalex.org/F4320322804","display_name":"Deanship of Scientific Research, King Faisal University","ror":"https://ror.org/00dn43547"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280636005.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W116352313","https://openalex.org/W1930107487","https://openalex.org/W1965556558","https://openalex.org/W1972928524","https://openalex.org/W1980640266","https://openalex.org/W1982333395","https://openalex.org/W1983112381","https://openalex.org/W1990262501","https://openalex.org/W1996054349","https://openalex.org/W2008767786","https://openalex.org/W2018922010","https://openalex.org/W2023376510","https://openalex.org/W2045612986","https://openalex.org/W2069170668","https://openalex.org/W2079464502","https://openalex.org/W2329946076","https://openalex.org/W2766095945","https://openalex.org/W2799234579","https://openalex.org/W2913455742","https://openalex.org/W2963064565","https://openalex.org/W2988840159","https://openalex.org/W2994831758","https://openalex.org/W3004024091","https://openalex.org/W3014272419","https://openalex.org/W3095343625","https://openalex.org/W3099958155","https://openalex.org/W4233886660","https://openalex.org/W6652592899","https://openalex.org/W6721560102","https://openalex.org/W6771949933"],"related_works":["https://openalex.org/W3135342338","https://openalex.org/W1994650426","https://openalex.org/W4388477834","https://openalex.org/W2139202366","https://openalex.org/W2983843394","https://openalex.org/W2946141653","https://openalex.org/W2142956537","https://openalex.org/W2156045615","https://openalex.org/W4288024380","https://openalex.org/W2988840159"],"abstract_inverted_index":{"The":[0,20],"functions":[1],"1+z,":[2],"ez,":[3],"1+Az,":[4,74],"A\u2208(0,1]":[5],"map":[6],"the":[7,18,49,56,69,88],"unit":[8],"disc":[9],"D":[10],"to":[11,87],"a":[12,28],"domain":[13],"which":[14,55,85],"is":[15,27,38],"symmetric":[16,39],"about":[17,40],"x-axis.":[19],"Regular":[21,92],"Coulomb":[22,93],"wave":[23,94],"function":[24,29],"(RCWF)":[25],"FL,\u03b7":[26,37,61],"involving":[30,81],"two":[31],"parameters":[32],"L":[33,51],"and":[34,36,52,73],"\u03b7,":[35],"these.":[41],"In":[42],"this":[43],"article,":[44],"we":[45],"derive":[46],"conditions":[47],"on":[48],"parameter":[50],"\u03b7":[53],"for":[54],"normalized":[57,91],"form":[58],"fL":[59],"of":[60,90],"are":[62,83],"subordinated":[63],"by":[64,71],"1+z.":[65],"We":[66],"also":[67],"consider":[68],"subordination":[70,79],"ez":[72],"A\u2208(0,1].":[75],"A":[76],"few":[77],"more":[78],"properties":[80],"RCWF":[82],"discussed,":[84],"leads":[86],"star-likeness":[89],"functions.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
