Some alternating double sum formulae of multiple zeta values
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300004 |
Resumo: | In this paper, we produce shuffle relations from multiple zeta values of the form ζ ({ 1 }m-1, n+1). Here { 1 }k is k repetitions of 1, and for a string of positive integers α1, α2, ...,αr with αr > 2 . ζ (α1, α1, ..., α1) = Σ n1-α1n2-α2... n r-αr 1 < n1 < n2 < ... < n r As applications of the sum formula and a newly developed weighted sum formula, we shall prove for even integers k, r > 0 that k r Σ Σ (-1)ℓ Σ ζ (α0, α1, ..., αj + βj, βj+1, ..., βk, βk+1 + 1) j = 0 ℓ = 0 |α| = j + r - ℓ + 1 |β| = k - j + ℓ + 2 + Σ Σ ζ (α0, α1, ..., αk r - ℓ + 3) = ζ (k + r + 4). 0 < ℓ < r |α| = k + ℓ + 1 ℓ : even Mathematical subject classification: Primary: 40A25, 40B05; Secondary: 11M99, 33E99. |
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Some alternating double sum formulae of multiple zeta valuesmultiple zeta valuessum formulaeIn this paper, we produce shuffle relations from multiple zeta values of the form ζ ({ 1 }m-1, n+1). Here { 1 }k is k repetitions of 1, and for a string of positive integers α1, α2, ...,αr with αr > 2 . ζ (α1, α1, ..., α1) = Σ n1-α1n2-α2... n r-αr 1 < n1 < n2 < ... < n r As applications of the sum formula and a newly developed weighted sum formula, we shall prove for even integers k, r > 0 that k r Σ Σ (-1)ℓ Σ ζ (α0, α1, ..., αj + βj, βj+1, ..., βk, βk+1 + 1) j = 0 ℓ = 0 |α| = j + r - ℓ + 1 |β| = k - j + ℓ + 2 + Σ Σ ζ (α0, α1, ..., αk r - ℓ + 3) = ζ (k + r + 4). 0 < ℓ < r |α| = k + ℓ + 1 ℓ : even Mathematical subject classification: Primary: 40A25, 40B05; Secondary: 11M99, 33E99.Sociedade Brasileira de Matemática Aplicada e Computacional2010-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300004Computational & Applied Mathematics v.29 n.3 2010reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022010000300004info:eu-repo/semantics/openAccessEie,MinkingYang,Fu-YaoOng,Yao Lineng2010-11-22T00:00:00Zoai:scielo:S1807-03022010000300004Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2010-11-22T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
Some alternating double sum formulae of multiple zeta values |
title |
Some alternating double sum formulae of multiple zeta values |
spellingShingle |
Some alternating double sum formulae of multiple zeta values Eie,Minking multiple zeta values sum formulae |
title_short |
Some alternating double sum formulae of multiple zeta values |
title_full |
Some alternating double sum formulae of multiple zeta values |
title_fullStr |
Some alternating double sum formulae of multiple zeta values |
title_full_unstemmed |
Some alternating double sum formulae of multiple zeta values |
title_sort |
Some alternating double sum formulae of multiple zeta values |
author |
Eie,Minking |
author_facet |
Eie,Minking Yang,Fu-Yao Ong,Yao Lin |
author_role |
author |
author2 |
Yang,Fu-Yao Ong,Yao Lin |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Eie,Minking Yang,Fu-Yao Ong,Yao Lin |
dc.subject.por.fl_str_mv |
multiple zeta values sum formulae |
topic |
multiple zeta values sum formulae |
description |
In this paper, we produce shuffle relations from multiple zeta values of the form ζ ({ 1 }m-1, n+1). Here { 1 }k is k repetitions of 1, and for a string of positive integers α1, α2, ...,αr with αr > 2 . ζ (α1, α1, ..., α1) = Σ n1-α1n2-α2... n r-αr 1 < n1 < n2 < ... < n r As applications of the sum formula and a newly developed weighted sum formula, we shall prove for even integers k, r > 0 that k r Σ Σ (-1)ℓ Σ ζ (α0, α1, ..., αj + βj, βj+1, ..., βk, βk+1 + 1) j = 0 ℓ = 0 |α| = j + r - ℓ + 1 |β| = k - j + ℓ + 2 + Σ Σ ζ (α0, α1, ..., αk r - ℓ + 3) = ζ (k + r + 4). 0 < ℓ < r |α| = k + ℓ + 1 ℓ : even Mathematical subject classification: Primary: 40A25, 40B05; Secondary: 11M99, 33E99. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300004 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1807-03022010000300004 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
Computational & Applied Mathematics v.29 n.3 2010 reponame:Computational & Applied Mathematics instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
Computational & Applied Mathematics |
collection |
Computational & Applied Mathematics |
repository.name.fl_str_mv |
Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) |
repository.mail.fl_str_mv |
||sbmac@sbmac.org.br |
_version_ |
1754734890220257280 |