Alternating double t-values and T-values

Abstract Recently, Hoffman (Commun. Number Theory Phys. 13:529–567, 2019), Kaneko and Tsumura (Tsukuba J. Math. (in press), 2020) introduced and systematically studied two variants of multiple zeta values of level two, i.e., multiple t-values and multiple T-values, respectively. In this paper, by th...

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Main Author:	Junjie Quan
Format:	Article
Language:	English
Published:	SpringerOpen 2020-08-01
Series:	Advances in Difference Equations
Subjects:	Multiple zeta values Multiple t-values Multiple T-values Odd harmonic numbers Contour integration
Online Access:	http://link.springer.com/article/10.1186/s13662-020-02917-1

id	doaj-b394af503fec4235ad3d992233491569
record_format	Article
spelling	doaj-b394af503fec4235ad3d9922334915692020-11-25T03:35:00ZengSpringerOpenAdvances in Difference Equations1687-18472020-08-012020111310.1186/s13662-020-02917-1Alternating double t-values and T-valuesJunjie Quan0School of Information Science and Technology, Xiamen University Tan Kah Kee CollegeAbstract Recently, Hoffman (Commun. Number Theory Phys. 13:529–567, 2019), Kaneko and Tsumura (Tsukuba J. Math. (in press), 2020) introduced and systematically studied two variants of multiple zeta values of level two, i.e., multiple t-values and multiple T-values, respectively. In this paper, by the contour integration and residue theorem, we establish two general identities, which further reduce to the expressions of the alternating double t-values and T-values. Some examples are also provided.http://link.springer.com/article/10.1186/s13662-020-02917-1Multiple zeta valuesMultiple t-valuesMultiple T-valuesOdd harmonic numbersContour integration
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Junjie Quan
spellingShingle	Junjie Quan Alternating double t-values and T-values Advances in Difference Equations Multiple zeta values Multiple t-values Multiple T-values Odd harmonic numbers Contour integration
author_facet	Junjie Quan
author_sort	Junjie Quan
title	Alternating double t-values and T-values
title_short	Alternating double t-values and T-values
title_full	Alternating double t-values and T-values
title_fullStr	Alternating double t-values and T-values
title_full_unstemmed	Alternating double t-values and T-values
title_sort	alternating double t-values and t-values
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-08-01
description	Abstract Recently, Hoffman (Commun. Number Theory Phys. 13:529–567, 2019), Kaneko and Tsumura (Tsukuba J. Math. (in press), 2020) introduced and systematically studied two variants of multiple zeta values of level two, i.e., multiple t-values and multiple T-values, respectively. In this paper, by the contour integration and residue theorem, we establish two general identities, which further reduce to the expressions of the alternating double t-values and T-values. Some examples are also provided.
topic	Multiple zeta values Multiple t-values Multiple T-values Odd harmonic numbers Contour integration
url	http://link.springer.com/article/10.1186/s13662-020-02917-1
work_keys_str_mv	AT junjiequan alternatingdoubletvaluesandtvalues
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Alternating double t-values and T-values

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