A combinatorial identity and applications

Autores
Ferrari, Mariano Andrés; Panzone, Pablo Andres
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An identity for the finite sum 1^N rac{z^n}{q^n-r} is given. Related sums (or series) were studied  by Scherk, Clausen, Ramanujan, Shanks, Andrews and others. We use such identity  to give  new   formulas for sum_1^infty rac{z^n}{q^n-r}, the Riemann zeta function and Euler-Mascheroni constant. An  irrationality result is also proved.
Fil: Ferrari, Mariano Andrés. Universidad Nacional de la Patagonia; Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina;
Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina; Universidad Nacional del Sur; Argentina;
Materia
COMBINATORIAL IDENTITY
IRRATIONALITIES
RIEMANN ZETA FUNCTION
EULER-MASCHERONI CONSTANT
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:11336/1942
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/1942
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A combinatorial identity and applicationsFerrari, Mariano AndrésPanzone, Pablo AndresCOMBINATORIAL IDENTITYIRRATIONALITIESRIEMANN ZETA FUNCTIONEULER-MASCHERONI CONSTANThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1An identity for the finite sum 1^N rac{z^n}{q^n-r} is given. Related sums (or series) were studied  by Scherk, Clausen, Ramanujan, Shanks, Andrews and others. We use such identity  to give  new   formulas for sum_1^infty rac{z^n}{q^n-r}, the Riemann zeta function and Euler-Mascheroni constant. An  irrationality result is also proved.Fil: Ferrari, Mariano Andrés. Universidad Nacional de la Patagonia; Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina;Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina; Universidad Nacional del Sur; Argentina;Unión Matemática Argentina2013-05-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/1942Ferrari, Mariano Andrés; Panzone, Pablo Andres; A combinatorial identity and applications; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 54; 1; 29-5-2013; 35-420041-69321669-9637enginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v54n1/v54n1a04.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:13:28Zoai:ri.conicet.gov.ar:11336/1942instacron: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:34982025-09-29 10:13:28.723CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A combinatorial identity and applications
title A combinatorial identity and applications
spellingShingle A combinatorial identity and applications
Ferrari, Mariano Andrés
COMBINATORIAL IDENTITY
IRRATIONALITIES
RIEMANN ZETA FUNCTION
EULER-MASCHERONI CONSTANT
title_short A combinatorial identity and applications
title_full A combinatorial identity and applications
title_fullStr A combinatorial identity and applications
title_full_unstemmed A combinatorial identity and applications
title_sort A combinatorial identity and applications
dc.creator.none.fl_str_mv Ferrari, Mariano Andrés
Panzone, Pablo Andres
author Ferrari, Mariano Andrés
author_facet Ferrari, Mariano Andrés
Panzone, Pablo Andres
author_role author
author2 Panzone, Pablo Andres
author2_role author
dc.subject.none.fl_str_mv COMBINATORIAL IDENTITY
IRRATIONALITIES
RIEMANN ZETA FUNCTION
EULER-MASCHERONI CONSTANT
topic COMBINATORIAL IDENTITY
IRRATIONALITIES
RIEMANN ZETA FUNCTION
EULER-MASCHERONI CONSTANT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv An identity for the finite sum 1^N rac{z^n}{q^n-r} is given. Related sums (or series) were studied  by Scherk, Clausen, Ramanujan, Shanks, Andrews and others. We use such identity  to give  new   formulas for sum_1^infty rac{z^n}{q^n-r}, the Riemann zeta function and Euler-Mascheroni constant. An  irrationality result is also proved.
Fil: Ferrari, Mariano Andrés. Universidad Nacional de la Patagonia; Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina;
Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina; Universidad Nacional del Sur; Argentina;
description An identity for the finite sum 1^N rac{z^n}{q^n-r} is given. Related sums (or series) were studied  by Scherk, Clausen, Ramanujan, Shanks, Andrews and others. We use such identity  to give  new   formulas for sum_1^infty rac{z^n}{q^n-r}, the Riemann zeta function and Euler-Mascheroni constant. An  irrationality result is also proved.
publishDate 2013
dc.date.none.fl_str_mv 2013-05-29
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/11336/1942
Ferrari, Mariano Andrés; Panzone, Pablo Andres; A combinatorial identity and applications; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 54; 1; 29-5-2013; 35-42
0041-6932
1669-9637
url http://hdl.handle.net/11336/1942
identifier_str_mv Ferrari, Mariano Andrés; Panzone, Pablo Andres; A combinatorial identity and applications; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 54; 1; 29-5-2013; 35-42
0041-6932
1669-9637
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v54n1/v54n1a04.pdf
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 Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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 13.070432

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