Derivatives of Horn hypergeometric functions with respect to their parameters

Autores
Ancarani, L. U.; del Punta, Jessica Adriana; Gasaneo, Gustavo
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn's functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction.
Fil: Ancarani, L. U.. Université de Lorraine; Francia
Fil: del Punta, Jessica Adriana. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Université de Lorraine; Francia
Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Materia
HORN HYPERGEOMETRIC FUNCTIONS
DERIVATIVES
PARAMETERS
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:11336/64180
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Derivatives of Horn hypergeometric functions with respect to their parametersAncarani, L. U.del Punta, Jessica AdrianaGasaneo, GustavoHORN HYPERGEOMETRIC FUNCTIONSDERIVATIVESPARAMETERShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn's functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction.Fil: Ancarani, L. U.. Université de Lorraine; FranciaFil: del Punta, Jessica Adriana. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Université de Lorraine; FranciaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaAmerican Institute of Physics2017-07-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/64180Ancarani, L. U.; del Punta, Jessica Adriana; Gasaneo, Gustavo; Derivatives of Horn hypergeometric functions with respect to their parameters; American Institute of Physics; Journal of Mathematical Physics; 58; 7; 24-7-2017; 1-18; 0735040022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.4994059info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4994059info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1712.07579info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:54:36Zoai:ri.conicet.gov.ar:11336/64180instacron: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 09:54:36.345CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Derivatives of Horn hypergeometric functions with respect to their parameters
title Derivatives of Horn hypergeometric functions with respect to their parameters
spellingShingle Derivatives of Horn hypergeometric functions with respect to their parameters
Ancarani, L. U.
HORN HYPERGEOMETRIC FUNCTIONS
DERIVATIVES
PARAMETERS
title_short Derivatives of Horn hypergeometric functions with respect to their parameters
title_full Derivatives of Horn hypergeometric functions with respect to their parameters
title_fullStr Derivatives of Horn hypergeometric functions with respect to their parameters
title_full_unstemmed Derivatives of Horn hypergeometric functions with respect to their parameters
title_sort Derivatives of Horn hypergeometric functions with respect to their parameters
dc.creator.none.fl_str_mv Ancarani, L. U.
del Punta, Jessica Adriana
Gasaneo, Gustavo
author Ancarani, L. U.
author_facet Ancarani, L. U.
del Punta, Jessica Adriana
Gasaneo, Gustavo
author_role author
author2 del Punta, Jessica Adriana
Gasaneo, Gustavo
author2_role author
author
dc.subject.none.fl_str_mv HORN HYPERGEOMETRIC FUNCTIONS
DERIVATIVES
PARAMETERS
topic HORN HYPERGEOMETRIC FUNCTIONS
DERIVATIVES
PARAMETERS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn's functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction.
Fil: Ancarani, L. U.. Université de Lorraine; Francia
Fil: del Punta, Jessica Adriana. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Université de Lorraine; Francia
Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
description The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn's functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction.
publishDate 2017
dc.date.none.fl_str_mv 2017-07-24
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/11336/64180
Ancarani, L. U.; del Punta, Jessica Adriana; Gasaneo, Gustavo; Derivatives of Horn hypergeometric functions with respect to their parameters; American Institute of Physics; Journal of Mathematical Physics; 58; 7; 24-7-2017; 1-18; 073504
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/64180
identifier_str_mv Ancarani, L. U.; del Punta, Jessica Adriana; Gasaneo, Gustavo; Derivatives of Horn hypergeometric functions with respect to their parameters; American Institute of Physics; Journal of Mathematical Physics; 58; 7; 24-7-2017; 1-18; 073504
0022-2488
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4994059
info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4994059
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1712.07579
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 American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
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 13.13397

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