{"id":"https://openalex.org/W2069368864","doi":"https://doi.org/10.1137/s0036142901387385","title":"The Zeros of Special Functions from a Fixed Point Method","display_name":"The Zeros of Special Functions from a Fixed Point Method","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2069368864","doi":"https://doi.org/10.1137/s0036142901387385","mag":"2069368864"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901387385","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901387385","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5060535118","display_name":"Javier Segura","orcid":"https://orcid.org/0000-0002-0841-5636"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Javier Segura","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060535118"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0611,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.9394822,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"40","issue":"1","first_page":"114","last_page":"133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9983000159263611,"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":0.9983000159263611,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983000159263611,"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":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8807883858680725},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5914084911346436},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4735155403614044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45627301931381226},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4219295382499695},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4191739857196808},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3712766766548157},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3561769723892212},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3203005790710449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8807883858680725},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5914084911346436},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4735155403614044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45627301931381226},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4219295382499695},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4191739857196808},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3712766766548157},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3561769723892212},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3203005790710449},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142901387385","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901387385","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1524098039","https://openalex.org/W1585093618","https://openalex.org/W1656166924","https://openalex.org/W1985468919","https://openalex.org/W1996054349","https://openalex.org/W1996160600","https://openalex.org/W2006547000","https://openalex.org/W2008754992","https://openalex.org/W2008767786","https://openalex.org/W2015773120","https://openalex.org/W2016959251","https://openalex.org/W2040185255","https://openalex.org/W2053289371","https://openalex.org/W2057938864","https://openalex.org/W2081633643","https://openalex.org/W2082546918","https://openalex.org/W2116030792","https://openalex.org/W2125978368","https://openalex.org/W2147559715","https://openalex.org/W2158584153","https://openalex.org/W2165106817","https://openalex.org/W2321101418","https://openalex.org/W2324379530","https://openalex.org/W2737751924","https://openalex.org/W2801179766","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W4383100562","https://openalex.org/W175020571","https://openalex.org/W1965919058","https://openalex.org/W1628946225","https://openalex.org/W2323905825","https://openalex.org/W4294204420","https://openalex.org/W2952295687","https://openalex.org/W3083488279","https://openalex.org/W2980963558","https://openalex.org/W2952892835"],"abstract_inverted_index":{"A":[0],"scheme":[1,153],"for":[2,154],"the":[3,6,18,21,42,45,64,81,89,92,104,114,133,155,158,164],"computation":[4],"of":[5,8,20,32,34,44,52,63,83,88,99,103,119,121,157,160,163],"zeros":[7,82,118,134,159],"special":[9],"functions":[10,120],"and":[11,47,94,124,169],"orthogonal":[12],"polynomials":[13],"is":[14,56,86,96,106],"developed.":[15],"We":[16],"study":[17],"structure":[19,102],"first":[22],"order":[23,36,43],"difference-differential":[24],"equations":[25],"(DDEs)":[26],"satisfied":[27],"by":[28],"two":[29],"fundamental":[30],"sets":[31],"solutions":[33,46,162],"second":[35],"ODEs":[37],"$y_n^{\\prime\\prime}(x)+A_{n}(x)y_n":[38],"(x)=0$,":[39],"n":[40],"being":[41,80],"An":[48],"(x)":[49],"a":[50,60,97,136],"family":[51],"continuous":[53],"functions.":[54],"It":[55],"proved":[57],"that,":[58],"with":[59,75,142],"convenient":[61],"normalization":[62],"solutions,":[65],"$T_{\\pm1}(z)=z\\pm":[66],"\\mbox{\\rm":[67],"sign}(d)\\arctan(y_n":[68],"(x(z))/y_{n\\pm":[69],"1}(x(z)))$":[70],"are":[71],"globally":[72],"convergent":[73],"iterations":[74],"fixed":[76],"points":[77],"$z(x_n^{(i)})$,":[78],"$x_n^{(i)}$":[79],"yn(x);":[84],"d":[85],"one":[87],"coefficients":[90],"in":[91],"DDEs":[93,105],"z(x)":[95],"primitive":[98],"d.":[100],"The":[101],"also":[107],"used":[108],"to":[109,125,150],"set":[110],"global":[111],"bounds":[112],"on":[113],"differences":[115],"between":[116],"adjacent":[117],"consecutive":[122],"orders":[123],"find":[126],"iteration":[127],"steps":[128],"which":[129],"guarantee":[130],"that":[131],"all":[132],"inside":[135],"given":[137],"interval":[138],"can":[139],"be":[140],"found":[141],"certainty.":[143],"As":[144],"an":[145],"illustration,":[146],"we":[147],"describe":[148],"how":[149],"implement":[151],"this":[152],"calculation":[156],"arbitrary":[161],"Bessel,":[165],"Coulomb,":[166],"Legendre,":[167],"Hermite,":[168],"Laguerre":[170],"equations.":[171]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}