Numerical evaluation of Appell´s F1 hypergeometric function

Autores
Colavecchia, Flavio Dario; Gasaneo, Gustavo; Miraglia, Jorge Esteban
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we present a numerical scheme to compute the two-variable hypergeometric function F1(α,β,β′,γ;x,y) of Appell for complex parameters α,β,β′ and γ, and real values of the variables x and y. We implement a set of analytic continuations that allow us to obtain the F1 function outside the region of convergence of the series definition. These continuations can be written in terms of the Horn's G2 function, Appell's F2 function related, and the F1 hypergeometric itself. The computation of the function inside the region of convergence is achieved by two complementary methods. The first one involves a single-index series expansion of the F1 function, while the second one makes use of a numerical integration of a third order ordinary differential equation that represents the system of partial differential equations of the F1 function. We briefly sketch the program and show some examples of the numerical computation.
Fil: Colavecchia, Flavio Dario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Miraglia, Jorge Esteban. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Materia
Hypergeometric 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:11336/22373

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spelling Numerical evaluation of Appell´s F1 hypergeometric functionColavecchia, Flavio DarioGasaneo, GustavoMiraglia, Jorge EstebanHypergeometric Functionhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this work we present a numerical scheme to compute the two-variable hypergeometric function F1(α,β,β′,γ;x,y) of Appell for complex parameters α,β,β′ and γ, and real values of the variables x and y. We implement a set of analytic continuations that allow us to obtain the F1 function outside the region of convergence of the series definition. These continuations can be written in terms of the Horn's G2 function, Appell's F2 function related, and the F1 hypergeometric itself. The computation of the function inside the region of convergence is achieved by two complementary methods. The first one involves a single-index series expansion of the F1 function, while the second one makes use of a numerical integration of a third order ordinary differential equation that represents the system of partial differential equations of the F1 function. We briefly sketch the program and show some examples of the numerical computation.Fil: Colavecchia, Flavio Dario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Miraglia, Jorge Esteban. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaElsevier Science2001-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/22373Colavecchia, Flavio Dario; Gasaneo, Gustavo; Miraglia, Jorge Esteban; Numerical evaluation of Appell´s F1 hypergeometric function; Elsevier Science; Computer Physics Communications; 138; 1; 12-2001; 29-430010-4655CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0010465501001862info:eu-repo/semantics/altIdentifier/doi/10.1016/S0010-4655(01)00186-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:28Zoai:ri.conicet.gov.ar:11336/22373instacron: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:34982025-09-03 10:03:28.337CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical evaluation of Appell´s F1 hypergeometric function
title Numerical evaluation of Appell´s F1 hypergeometric function
spellingShingle Numerical evaluation of Appell´s F1 hypergeometric function
Colavecchia, Flavio Dario
Hypergeometric Function
title_short Numerical evaluation of Appell´s F1 hypergeometric function
title_full Numerical evaluation of Appell´s F1 hypergeometric function
title_fullStr Numerical evaluation of Appell´s F1 hypergeometric function
title_full_unstemmed Numerical evaluation of Appell´s F1 hypergeometric function
title_sort Numerical evaluation of Appell´s F1 hypergeometric function
dc.creator.none.fl_str_mv Colavecchia, Flavio Dario
Gasaneo, Gustavo
Miraglia, Jorge Esteban
author Colavecchia, Flavio Dario
author_facet Colavecchia, Flavio Dario
Gasaneo, Gustavo
Miraglia, Jorge Esteban
author_role author
author2 Gasaneo, Gustavo
Miraglia, Jorge Esteban
author2_role author
author
dc.subject.none.fl_str_mv Hypergeometric Function
topic Hypergeometric Function
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we present a numerical scheme to compute the two-variable hypergeometric function F1(α,β,β′,γ;x,y) of Appell for complex parameters α,β,β′ and γ, and real values of the variables x and y. We implement a set of analytic continuations that allow us to obtain the F1 function outside the region of convergence of the series definition. These continuations can be written in terms of the Horn's G2 function, Appell's F2 function related, and the F1 hypergeometric itself. The computation of the function inside the region of convergence is achieved by two complementary methods. The first one involves a single-index series expansion of the F1 function, while the second one makes use of a numerical integration of a third order ordinary differential equation that represents the system of partial differential equations of the F1 function. We briefly sketch the program and show some examples of the numerical computation.
Fil: Colavecchia, Flavio Dario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Miraglia, Jorge Esteban. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
description In this work we present a numerical scheme to compute the two-variable hypergeometric function F1(α,β,β′,γ;x,y) of Appell for complex parameters α,β,β′ and γ, and real values of the variables x and y. We implement a set of analytic continuations that allow us to obtain the F1 function outside the region of convergence of the series definition. These continuations can be written in terms of the Horn's G2 function, Appell's F2 function related, and the F1 hypergeometric itself. The computation of the function inside the region of convergence is achieved by two complementary methods. The first one involves a single-index series expansion of the F1 function, while the second one makes use of a numerical integration of a third order ordinary differential equation that represents the system of partial differential equations of the F1 function. We briefly sketch the program and show some examples of the numerical computation.
publishDate 2001
dc.date.none.fl_str_mv 2001-12
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/11336/22373
Colavecchia, Flavio Dario; Gasaneo, Gustavo; Miraglia, Jorge Esteban; Numerical evaluation of Appell´s F1 hypergeometric function; Elsevier Science; Computer Physics Communications; 138; 1; 12-2001; 29-43
0010-4655
CONICET Digital
CONICET
url http://hdl.handle.net/11336/22373
identifier_str_mv Colavecchia, Flavio Dario; Gasaneo, Gustavo; Miraglia, Jorge Esteban; Numerical evaluation of Appell´s F1 hypergeometric function; Elsevier Science; Computer Physics Communications; 138; 1; 12-2001; 29-43
0010-4655
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.sciencedirect.com/science/article/pii/S0010465501001862
info:eu-repo/semantics/altIdentifier/doi/10.1016/S0010-4655(01)00186-2
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 Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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