Two new approximants for the error function

Autores
Zaccari, Daniel Gustavo; Alturria Lanzardo, Carmina José; Pérez, Jorge; Cesco, Juan Carlos
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we present two new approximants for the Error Function. The starting point for obtaining them, is to use two alternative integral representations involving improper integrals. Both integrands include the function. Therefore, by replacing by its truncated Taylor's expansion, we obtain a rational approximant for which converges, for each x, to that function. Since these Taylor polynomials have simple roots, the improper integrals can be evaluated with the residues technique of integration in the complex plane, by using an appropriate contour of integration. By just using the roots of the polynomials, we get two new analytical expressions for the Error Function in terms of elementary functions. We show the behaviour of their corresponding errors by giving practical bounds for the absolute and relative errors, respectively.
Fil: Zaccari, Daniel Gustavo. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; Argentina
Fil: Alturria Lanzardo, Carmina José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina
Fil: Pérez, Jorge. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; Argentina
Fil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Materia
ERROR FUNCTION
COMPLEMENTARY ERROR FUNCTION
RESIDUES
CONTOUR OF INTEGRATION
RATIONAL APPROXIMANT
OSCILLATING INTEGRAL
INTEGRAL REPRESENTATION
BOYS FUNCTION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/183752
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Two new approximants for the error functionZaccari, Daniel GustavoAlturria Lanzardo, Carmina JoséPérez, JorgeCesco, Juan CarlosERROR FUNCTIONCOMPLEMENTARY ERROR FUNCTIONRESIDUESCONTOUR OF INTEGRATIONRATIONAL APPROXIMANTOSCILLATING INTEGRALINTEGRAL REPRESENTATIONBOYS FUNCTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we present two new approximants for the Error Function. The starting point for obtaining them, is to use two alternative integral representations involving improper integrals. Both integrands include the function. Therefore, by replacing by its truncated Taylor's expansion, we obtain a rational approximant for which converges, for each x, to that function. Since these Taylor polynomials have simple roots, the improper integrals can be evaluated with the residues technique of integration in the complex plane, by using an appropriate contour of integration. By just using the roots of the polynomials, we get two new analytical expressions for the Error Function in terms of elementary functions. We show the behaviour of their corresponding errors by giving practical bounds for the absolute and relative errors, respectively.Fil: Zaccari, Daniel Gustavo. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; ArgentinaFil: Alturria Lanzardo, Carmina José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; ArgentinaFil: Pérez, Jorge. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; ArgentinaFil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaScirea2019-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/183752Zaccari, Daniel Gustavo; Alturria Lanzardo, Carmina José; Pérez, Jorge; Cesco, Juan Carlos; Two new approximants for the error function; Scirea; Scirea Journal of Mathematics; 4; 4; 8-2019; 104-1142706-8862CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.scirea.org/journal/PaperInformation?PaperID=1425info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T14:34:06Zoai:ri.conicet.gov.ar:11336/183752instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982026-08-25 14:34:06.621CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Two new approximants for the error function
title Two new approximants for the error function
spellingShingle Two new approximants for the error function
Zaccari, Daniel Gustavo
ERROR FUNCTION
COMPLEMENTARY ERROR FUNCTION
RESIDUES
CONTOUR OF INTEGRATION
RATIONAL APPROXIMANT
OSCILLATING INTEGRAL
INTEGRAL REPRESENTATION
BOYS FUNCTION
title_short Two new approximants for the error function
title_full Two new approximants for the error function
title_fullStr Two new approximants for the error function
title_full_unstemmed Two new approximants for the error function
title_sort Two new approximants for the error function
dc.creator.none.fl_str_mv Zaccari, Daniel Gustavo
Alturria Lanzardo, Carmina José
Pérez, Jorge
Cesco, Juan Carlos
author Zaccari, Daniel Gustavo
author_facet Zaccari, Daniel Gustavo
Alturria Lanzardo, Carmina José
Pérez, Jorge
Cesco, Juan Carlos
author_role author
author2 Alturria Lanzardo, Carmina José
Pérez, Jorge
Cesco, Juan Carlos
author2_role author
author
author
dc.subject.none.fl_str_mv ERROR FUNCTION
COMPLEMENTARY ERROR FUNCTION
RESIDUES
CONTOUR OF INTEGRATION
RATIONAL APPROXIMANT
OSCILLATING INTEGRAL
INTEGRAL REPRESENTATION
BOYS FUNCTION
topic ERROR FUNCTION
COMPLEMENTARY ERROR FUNCTION
RESIDUES
CONTOUR OF INTEGRATION
RATIONAL APPROXIMANT
OSCILLATING INTEGRAL
INTEGRAL REPRESENTATION
BOYS FUNCTION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we present two new approximants for the Error Function. The starting point for obtaining them, is to use two alternative integral representations involving improper integrals. Both integrands include the function. Therefore, by replacing by its truncated Taylor's expansion, we obtain a rational approximant for which converges, for each x, to that function. Since these Taylor polynomials have simple roots, the improper integrals can be evaluated with the residues technique of integration in the complex plane, by using an appropriate contour of integration. By just using the roots of the polynomials, we get two new analytical expressions for the Error Function in terms of elementary functions. We show the behaviour of their corresponding errors by giving practical bounds for the absolute and relative errors, respectively.
Fil: Zaccari, Daniel Gustavo. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; Argentina
Fil: Alturria Lanzardo, Carmina José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina
Fil: Pérez, Jorge. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; Argentina
Fil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
description In this paper, we present two new approximants for the Error Function. The starting point for obtaining them, is to use two alternative integral representations involving improper integrals. Both integrands include the function. Therefore, by replacing by its truncated Taylor's expansion, we obtain a rational approximant for which converges, for each x, to that function. Since these Taylor polynomials have simple roots, the improper integrals can be evaluated with the residues technique of integration in the complex plane, by using an appropriate contour of integration. By just using the roots of the polynomials, we get two new analytical expressions for the Error Function in terms of elementary functions. We show the behaviour of their corresponding errors by giving practical bounds for the absolute and relative errors, respectively.
publishDate 2019
dc.date.none.fl_str_mv 2019-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/183752
Zaccari, Daniel Gustavo; Alturria Lanzardo, Carmina José; Pérez, Jorge; Cesco, Juan Carlos; Two new approximants for the error function; Scirea; Scirea Journal of Mathematics; 4; 4; 8-2019; 104-114
2706-8862
CONICET Digital
CONICET
url http://hdl.handle.net/11336/183752
identifier_str_mv Zaccari, Daniel Gustavo; Alturria Lanzardo, Carmina José; Pérez, Jorge; Cesco, Juan Carlos; Two new approximants for the error function; Scirea; Scirea Journal of Mathematics; 4; 4; 8-2019; 104-114
2706-8862
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.scirea.org/journal/PaperInformation?PaperID=1425
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Scirea
publisher.none.fl_str_mv Scirea
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.265058

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