Multiple zeta star values on 3–2–1 indices
In 2008, Muneta found explicit evaluation of the multiple zeta star value ζ ⋆ ( { 3 , 1 } d ) , and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3–2–1 indices. In this paper, we provide another way of deriving the formulas mentioned above. It is based on our previous work...
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| Veröffentlicht in: | The Ramanujan journal 2023, Vol.60 (1), p.259-285 |
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| creator | Hessami Pilehrood, Kh Pilehrood, T. Hessami |
| description | In 2008, Muneta found explicit evaluation of the multiple zeta star value
ζ
⋆
(
{
3
,
1
}
d
)
, and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3–2–1 indices. In this paper, we provide another way of deriving the formulas mentioned above. It is based on our previous work on generating functions for multiple zeta star values and also on constructions of generating functions for restricted sums of alternating Euler sums. As a result, the formulas obtained are simpler and computationally more effective than the known ones. Moreover, we give explicit evaluations of
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
)
and
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
,
{
2
}
m
+
1
)
, which are new and have not appeared in the literature before. |
| doi_str_mv | 10.1007/s11139-022-00642-9 |
| format | Article |
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ζ
⋆
(
{
3
,
1
}
d
)
, and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3–2–1 indices. In this paper, we provide another way of deriving the formulas mentioned above. It is based on our previous work on generating functions for multiple zeta star values and also on constructions of generating functions for restricted sums of alternating Euler sums. As a result, the formulas obtained are simpler and computationally more effective than the known ones. Moreover, we give explicit evaluations of
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
)
and
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
,
{
2
}
m
+
1
)
, which are new and have not appeared in the literature before.</description><identifier>ISSN: 1382-4090</identifier><identifier>EISSN: 1572-9303</identifier><identifier>DOI: 10.1007/s11139-022-00642-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Field Theory and Polynomials ; Fourier Analysis ; Functions of a Complex Variable ; Mathematics ; Mathematics and Statistics ; Number Theory ; Sums</subject><ispartof>The Ramanujan journal, 2023, Vol.60 (1), p.259-285</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-bf228eff1ffdfa4737982d50e4b07ccbf75892fd4594fa7d14ded0372597c2e13</citedby><cites>FETCH-LOGICAL-c319t-bf228eff1ffdfa4737982d50e4b07ccbf75892fd4594fa7d14ded0372597c2e13</cites><orcidid>0000-0002-8429-3490</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11139-022-00642-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11139-022-00642-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Hessami Pilehrood, Kh</creatorcontrib><creatorcontrib>Pilehrood, T. Hessami</creatorcontrib><title>Multiple zeta star values on 3–2–1 indices</title><title>The Ramanujan journal</title><addtitle>Ramanujan J</addtitle><description>In 2008, Muneta found explicit evaluation of the multiple zeta star value
ζ
⋆
(
{
3
,
1
}
d
)
, and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3–2–1 indices. In this paper, we provide another way of deriving the formulas mentioned above. It is based on our previous work on generating functions for multiple zeta star values and also on constructions of generating functions for restricted sums of alternating Euler sums. As a result, the formulas obtained are simpler and computationally more effective than the known ones. Moreover, we give explicit evaluations of
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
)
and
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
,
{
2
}
m
+
1
)
, which are new and have not appeared in the literature before.</description><subject>Combinatorics</subject><subject>Field Theory and Polynomials</subject><subject>Fourier Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Sums</subject><issn>1382-4090</issn><issn>1572-9303</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9ULtOxDAQtBBIHAc_QBWJ2sd67ZzjEp2AQzpEA7Xl-IFyCkmwc0hQ8Q_8IV-CIUh0FKudYmZ2dgg5ZbBgAPI8Mca4ooBIAZYCqdojM1bKDDjw_Yx5hVSAgkNylNIWAARwOSOL2107NkPrizc_miKNJhYvpt35VPRdwT_fPzAPK5rONdanY3IQTJv8ye-ek4ery_vVmm7urm9WFxtqOVMjrQNi5UNgIbhghORSVehK8KIGaW0dZFkpDE6USgQjHRPOu5wHSyUtesbn5GzyHWL_nMOMetvvYpdPapRLqPKLsswsnFg29ilFH_QQmycTXzUD_d2LnnrRuRf904tWWcQnUcrk7tHHP-t_VF9AdGWm</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Hessami Pilehrood, Kh</creator><creator>Pilehrood, T. Hessami</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-8429-3490</orcidid></search><sort><creationdate>2023</creationdate><title>Multiple zeta star values on 3–2–1 indices</title><author>Hessami Pilehrood, Kh ; Pilehrood, T. Hessami</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-bf228eff1ffdfa4737982d50e4b07ccbf75892fd4594fa7d14ded0372597c2e13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Combinatorics</topic><topic>Field Theory and Polynomials</topic><topic>Fourier Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Sums</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hessami Pilehrood, Kh</creatorcontrib><creatorcontrib>Pilehrood, T. Hessami</creatorcontrib><collection>CrossRef</collection><jtitle>The Ramanujan journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hessami Pilehrood, Kh</au><au>Pilehrood, T. Hessami</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiple zeta star values on 3–2–1 indices</atitle><jtitle>The Ramanujan journal</jtitle><stitle>Ramanujan J</stitle><date>2023</date><risdate>2023</risdate><volume>60</volume><issue>1</issue><spage>259</spage><epage>285</epage><pages>259-285</pages><issn>1382-4090</issn><eissn>1572-9303</eissn><abstract>In 2008, Muneta found explicit evaluation of the multiple zeta star value
ζ
⋆
(
{
3
,
1
}
d
)
, and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3–2–1 indices. In this paper, we provide another way of deriving the formulas mentioned above. It is based on our previous work on generating functions for multiple zeta star values and also on constructions of generating functions for restricted sums of alternating Euler sums. As a result, the formulas obtained are simpler and computationally more effective than the known ones. Moreover, we give explicit evaluations of
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
)
and
ζ
⋆
(
{
{
2
}
m
,
3
,
{
2
}
m
,
1
}
d
,
{
2
}
m
+
1
)
, which are new and have not appeared in the literature before.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11139-022-00642-9</doi><tpages>27</tpages><orcidid>https://orcid.org/0000-0002-8429-3490</orcidid></addata></record> |
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| ispartof | The Ramanujan journal, 2023, Vol.60 (1), p.259-285 |
| issn | 1382-4090 1572-9303 |
| language | eng |
| recordid | cdi_proquest_journals_2760864275 |
| source | SpringerLink Journals |
| subjects | Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory Sums |
| title | Multiple zeta star values on 3–2–1 indices |
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