{"id":"https://openalex.org/W2098376053","doi":"https://doi.org/10.1080/00207169508804391","title":"On the legendre coefficients of the moments of the general order derivative of an infinitely differentiable function","display_name":"On the legendre coefficients of the moments of the general order derivative of an infinitely differentiable function","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2098376053","doi":"https://doi.org/10.1080/00207169508804391","mag":"2098376053"},"language":"en","primary_location":{"id":"doi:10.1080/00207169508804391","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804391","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016529266","display_name":"E. H. Doha","orcid":"https://orcid.org/0000-0002-7781-6871"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"E. H. Doha","raw_affiliation_strings":["Department of Mathematics, Faculty of Science , Cairo University , Giza, Egypt","Department of Mathematics, Faculty of Science , Cairo University , Giza , Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science , Cairo University , Giza, Egypt","institution_ids":["https://openalex.org/I145487455"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science , Cairo University , Giza , Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077416253","display_name":"S. I. El-Soubhy","orcid":"https://orcid.org/0000-0003-3088-1788"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. I. El-Soubhy","raw_affiliation_strings":["Department of Mathematics , Girl's College of Education , Jeddah, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Girl's College of Education , Jeddah, Saudi Arabia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016529266"],"corresponding_institution_ids":["https://openalex.org/I145487455"],"apc_list":null,"apc_paid":null,"fwci":0.5491,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.68108108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"56","issue":"1-2","first_page":"107","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9462000131607056,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9462000131607056,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9397000074386597,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9193999767303467,"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/legendre-polynomials","display_name":"Legendre polynomials","score":0.89955735206604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8431761264801025},{"id":"https://openalex.org/keywords/legendre-function","display_name":"Legendre function","score":0.8224923610687256},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6146031618118286},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.5582361817359924},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.540981650352478},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.485245943069458},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4823572039604187},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4813166856765747},{"id":"https://openalex.org/keywords/associated-legendre-polynomials","display_name":"Associated Legendre polynomials","score":0.48020467162132263},{"id":"https://openalex.org/keywords/legendre-transformation","display_name":"Legendre transformation","score":0.4738600552082062},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.46806564927101135},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4598442316055298},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.43264830112457275},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3658393621444702},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.0811784565448761},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.06586101651191711},{"id":"https://openalex.org/keywords/gegenbauer-polynomials","display_name":"Gegenbauer polynomials","score":0.05149918794631958}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.89955735206604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8431761264801025},{"id":"https://openalex.org/C153262748","wikidata":"https://www.wikidata.org/wiki/Q17098449","display_name":"Legendre function","level":3,"score":0.8224923610687256},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6146031618118286},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.5582361817359924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.540981650352478},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.485245943069458},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4823572039604187},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4813166856765747},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.48020467162132263},{"id":"https://openalex.org/C116594300","wikidata":"https://www.wikidata.org/wiki/Q908652","display_name":"Legendre transformation","level":2,"score":0.4738600552082062},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.46806564927101135},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4598442316055298},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.43264830112457275},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3658393621444702},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0811784565448761},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.06586101651191711},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.05149918794631958},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.0},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":1,"locations":[{"id":"doi:10.1080/00207169508804391","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804391","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W140628048","https://openalex.org/W906146811","https://openalex.org/W1574656040","https://openalex.org/W1912930600","https://openalex.org/W1969307568","https://openalex.org/W1978937644","https://openalex.org/W1980374758","https://openalex.org/W1984700819","https://openalex.org/W1987634257","https://openalex.org/W1988546126","https://openalex.org/W1989768884","https://openalex.org/W2002628574","https://openalex.org/W2005184360","https://openalex.org/W2009466983","https://openalex.org/W2025226828","https://openalex.org/W2036494998","https://openalex.org/W2050909389","https://openalex.org/W2054796168","https://openalex.org/W2061078256","https://openalex.org/W2063055382","https://openalex.org/W2064350296","https://openalex.org/W2066402621","https://openalex.org/W2075454166","https://openalex.org/W2090590186","https://openalex.org/W2136807431","https://openalex.org/W2143781224","https://openalex.org/W2408478130","https://openalex.org/W4248145103","https://openalex.org/W4298060601","https://openalex.org/W6605696395"],"related_works":["https://openalex.org/W2953361964","https://openalex.org/W3005861762","https://openalex.org/W3020087995","https://openalex.org/W2025296287","https://openalex.org/W2379187670","https://openalex.org/W2736737644","https://openalex.org/W2217115449","https://openalex.org/W2385225694","https://openalex.org/W4246417956","https://openalex.org/W2061262082"],"abstract_inverted_index":{"Formulae":[0],"for":[1,35],"the":[2,6,9,53,61,65],"Legendre":[3,22,54],"coefficients":[4,23,56],"of":[5,8,13,20,29,49,68],"moments":[7],"general":[10],"order":[11,51],"derivative":[12],"an":[14],"infinitely":[15],"differentiable":[16],"function":[17],"in":[18,52],"terms":[19],"its":[21],"are":[24,57,71],"derived.":[25],"Two":[26],"numerical":[27],"applications":[28],"how":[30],"to":[31,46],"use":[32],"these":[33],"formulae":[34],"solving":[36],"ordinary":[37],"differential":[38],"equations":[39],"with":[40,60],"varying":[41],"coefficients,":[42],"by":[43,64],"reducing":[44],"them":[45],"recurrence":[47],"relations":[48],"lowest":[50],"expansion":[55],"discussed.":[58],"Comparisons":[59],"results":[62],"obtained":[63],"optimal":[66],"algorithm":[67],"Lewanowicz":[69],"(1976)":[70],"made.":[72]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}