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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/22373
Ver los metadatos del registro completo
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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 |
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CONICET Digital (CONICET) |
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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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13.13397 |