{"id":"https://openalex.org/W3217578944","doi":"https://doi.org/10.3390/sym13122294","title":"A Survey of Some Recent Developments on Higher Transcendental Functions of Analytic Number Theory and Applied Mathematics","display_name":"A Survey of Some Recent Developments on Higher Transcendental Functions of Analytic Number Theory and Applied Mathematics","publication_year":2021,"publication_date":"2021-12-02","ids":{"openalex":"https://openalex.org/W3217578944","doi":"https://doi.org/10.3390/sym13122294","mag":"3217578944"},"language":"en","primary_location":{"id":"doi:10.3390/sym13122294","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122294","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2294/pdf?version=1638421881","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/2073-8994/13/12/2294/pdf?version=1638421881","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]},{"id":"https://openalex.org/I87490745","display_name":"Azerbaijan University","ror":"https://ror.org/00g1psz15","country_code":"AZ","type":"education","lineage":["https://openalex.org/I87490745"]}],"countries":["AZ","CA","IT","TW"],"is_corresponding":true,"raw_author_name":"Hari Mohan Srivastava","raw_affiliation_strings":["Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan","Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9277-8092","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan","institution_ids":["https://openalex.org/I87490745"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5079512627"],"corresponding_institution_ids":["https://openalex.org/I184693016","https://openalex.org/I212119943","https://openalex.org/I4210126829","https://openalex.org/I4210155399","https://openalex.org/I87490745"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":7.1792,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.98061389,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"13","issue":"12","first_page":"2294","last_page":"2294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"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":0.9984999895095825,"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"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9984999895095825,"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/transcendental-number","display_name":"Transcendental number","score":0.837613582611084},{"id":"https://openalex.org/keywords/transcendental-function","display_name":"Transcendental function","score":0.7995330095291138},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.5553629398345947},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5182123780250549},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5010969638824463},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4223122000694275},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3545153737068176},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3333205282688141},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10169193148612976}],"concepts":[{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.837613582611084},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.7995330095291138},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.5553629398345947},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5182123780250549},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5010969638824463},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4223122000694275},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3545153737068176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3333205282688141},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10169193148612976},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13122294","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122294","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2294/pdf?version=1638421881","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:52e1ad25ec564f6aac7ae8698edf125e","is_oa":true,"landing_page_url":"https://doaj.org/article/52e1ad25ec564f6aac7ae8698edf125e","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 13, Iss 12, p 2294 (2021)","raw_type":"article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/14466","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/14466","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/12/2294/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13122294","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; Volume 13; Issue 12; Pages: 2294","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13122294","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13122294","pdf_url":"https://www.mdpi.com/2073-8994/13/12/2294/pdf?version=1638421881","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":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.8799999952316284}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3217578944.pdf"},"referenced_works_count":87,"referenced_works":["https://openalex.org/W68100126","https://openalex.org/W191636288","https://openalex.org/W254209083","https://openalex.org/W433794350","https://openalex.org/W846923873","https://openalex.org/W1557530738","https://openalex.org/W1773067656","https://openalex.org/W1964441466","https://openalex.org/W1971828127","https://openalex.org/W1982261380","https://openalex.org/W2008295296","https://openalex.org/W2011690209","https://openalex.org/W2030974514","https://openalex.org/W2034789576","https://openalex.org/W2041616689","https://openalex.org/W2045350842","https://openalex.org/W2053757777","https://openalex.org/W2057246597","https://openalex.org/W2080572929","https://openalex.org/W2083967235","https://openalex.org/W2088652324","https://openalex.org/W2091714372","https://openalex.org/W2109175398","https://openalex.org/W2111280161","https://openalex.org/W2138446244","https://openalex.org/W2149155674","https://openalex.org/W2154393822","https://openalex.org/W2171447759","https://openalex.org/W2186872975","https://openalex.org/W2207710677","https://openalex.org/W2273134830","https://openalex.org/W2296779811","https://openalex.org/W2409068183","https://openalex.org/W2488797671","https://openalex.org/W2504078979","https://openalex.org/W2556784265","https://openalex.org/W2588588830","https://openalex.org/W2608565054","https://openalex.org/W2790185164","https://openalex.org/W2809988703","https://openalex.org/W2929379250","https://openalex.org/W2947935779","https://openalex.org/W2963641381","https://openalex.org/W2990918991","https://openalex.org/W2993571714","https://openalex.org/W2995639409","https://openalex.org/W2995812194","https://openalex.org/W3001106890","https://openalex.org/W3011722031","https://openalex.org/W3020959228","https://openalex.org/W3040229326","https://openalex.org/W3044959149","https://openalex.org/W3045819162","https://openalex.org/W3047751035","https://openalex.org/W3089672324","https://openalex.org/W3099063792","https://openalex.org/W3108269374","https://openalex.org/W3109634920","https://openalex.org/W3110149628","https://openalex.org/W3125811323","https://openalex.org/W3128811938","https://openalex.org/W3131923268","https://openalex.org/W3157840204","https://openalex.org/W3165460136","https://openalex.org/W3174386955","https://openalex.org/W3198172853","https://openalex.org/W3201136098","https://openalex.org/W4230104858","https://openalex.org/W4230310314","https://openalex.org/W4231695981","https://openalex.org/W4238188161","https://openalex.org/W4242849907","https://openalex.org/W4252810189","https://openalex.org/W4297901428","https://openalex.org/W4389487827","https://openalex.org/W6609593801","https://openalex.org/W6637895426","https://openalex.org/W6643006538","https://openalex.org/W6686924045","https://openalex.org/W6688153269","https://openalex.org/W6693943217","https://openalex.org/W6722323958","https://openalex.org/W6730176618","https://openalex.org/W6771593766","https://openalex.org/W6786853936","https://openalex.org/W6800954668","https://openalex.org/W7067911713"],"related_works":["https://openalex.org/W1481108397","https://openalex.org/W2120451642","https://openalex.org/W2314977061","https://openalex.org/W3183290492","https://openalex.org/W1792497233","https://openalex.org/W4378448846","https://openalex.org/W4300089223","https://openalex.org/W4387814077","https://openalex.org/W2523571232","https://openalex.org/W3014029144"],"abstract_inverted_index":{"Often":[0],"referred":[1],"to":[2,27,96,99,157],"as":[3,31],"special":[4],"functions":[5,22,74],"or":[6,177],"mathematical":[7,34,41],"functions,":[8,125,139],"the":[9,15,62,66,106,136,143,164,171,174,179,182],"origin":[10],"of":[11,14,19,59,61,68,110,116,135,142,161,173,181],"many":[12],"members":[13],"remarkably":[16],"vast":[17],"family":[18],"higher":[20,72,111,123,137],"transcendental":[21,73,112,124,138],"can":[23],"be":[24],"traced":[25],"back":[26],"such":[28],"widespread":[29],"areas":[30],"(for":[32],"example)":[33],"physics,":[35],"analytic":[36],"number":[37],"theory":[38,67,107],"and":[39,57,75,82,103,108],"applied":[40],"sciences.":[42],"Here,":[43],"in":[44,65,89,150,163],"this":[45,91,151],"survey-cum-expository":[46,152],"review":[47,153],"article,":[48,154],"we":[49,93,147],"aim":[50],"at":[51],"presenting":[52],"a":[53,159],"brief":[54],"introductory":[55],"overview":[56],"survey":[58],"some":[60],"recent":[63],"developments":[64],"several":[69],"extensively":[70],"studied":[71],"their":[76,128],"potential":[77],"applications.":[78],"For":[79],"further":[80],"reading":[81],"researching":[83],"by":[84],"those":[85,141],"who":[86],"are":[87,120,155],"interested":[88],"pursuing":[90],"subject,":[92],"have":[94,130,148],"chosen":[95],"provide":[97],"references":[98],"various":[100],"useful":[101],"monographs":[102],"textbooks":[104],"on":[105],"applications":[109],"functions.":[113],"Some":[114],"operators":[115],"fractional":[117],"calculus,":[118],"which":[119,146],"associated":[121],"with":[122,127],"together":[126],"applications,":[129],"also":[131],"been":[132],"considered.":[133],"Many":[134],"especially":[140],"hypergeometric":[144],"type,":[145],"investigated":[149],"known":[156],"display":[158],"kind":[160],"symmetry":[162],"sense":[165],"that":[166],"they":[167],"remain":[168],"invariant":[169],"when":[170,178],"order":[172,180],"numerator":[175],"parameters":[176,184],"denominator":[183],"is":[185],"arbitrarily":[186],"changed.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":31},{"year":2022,"cited_by_count":27},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}