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Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2016, Volume 68, Issue 4, pp. 1669 - 1694
...]. As applications we prove several conjectures involving multiple zeta star values (MZSV): the Two-one formula conjectured by Ohno and Zudilin, and a few conjectures of Imatomi et al... 
Multiple zeta values | Binomial sums | Multiple harmonic sums | Multiple zeta star values | Two-one formula | two-one formula | MATHEMATICS | multiple harmonic sums | SERIES | ANALOGS | multiple zeta values | binomial sums | multiple zeta star values
Journal Article
Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 2013, Volume 49, Issue 2, pp. 283 - 289
...) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star values and showed that this value is a rational multiple of a power of \pi... 
Multiple zeta values | Kondo-Saito-Tanaka theorem | Multiple zeta-star values | Harmonic algebra | Bowman-Bradley theorem | multiple zeta-star values | 11M32 | multiple zeta values | harmonic algebra | 05A15
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 12/2010, Volume 6, Issue 8, pp. 1927 - 1932
A duality-type relation for height one multiple zeta-star values is established. A conjectural generalization to the case of arbitrary height is also presented. 
Multiple zeta values | Riemann zeta values | MATHEMATICS
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 12/2012, Volume 8, Issue 8, pp. 1971 - 1976
.... In this paper, we show the corresponding relation for multiple zeta-star values by using partial-fractions expansion as Hoffman did. 
Hoffman's relation | Multiple zeta value | Multiple zeta-star value | MATHEMATICS | multiple zeta-star value
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 08/2013, Volume 9, Issue 5, pp. 1171 - 1184
In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2, …, 2... 
two-one formula | Multiple zeta values | multiple zeta-star values | MATHEMATICS | Mathematics - Number Theory
Journal Article
by Xu, Ce
Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 346, pp. 594 - 611
.... Then we apply it to obtain the closed forms of all quadratic Euler sums of weight ten. Furthermore, we also establish some relations between multiple zeta (star... 
Euler sum | Riemann zeta function | Multiple zeta (star) value | Multiple harmonic (star) sum | polylogarithm function | Harmonic number | INTEGRALS | MATHEMATICS, APPLIED | MULTIPLE ZETA VALUES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 1009 - 1042
.... We discuss the analytic representations of Euler sums through values of polylogarithm function and Riemann zeta function... 
Euler sums | Riemann zeta function | Multiple zeta (star) values | Stirling numbers | Harmonic numbers | Multiple harmonic (star) numbers | INTEGRALS | MATHEMATICS | MULTIPLE ZETA-VALUES | MATHEMATICS, APPLIED | SERIES
Journal Article
Journal of Algebra, ISSN 0021-8693, 07/2013, Volume 385, pp. 102 - 114
We define polynomials of one variable t whose values at t=0and1 are the multiple zeta values and the multiple zeta-star values, respectively... 
Multiple zeta values | Two-one conjecture | Multiple zeta-star values | Cyclic sum formula | Sum formula | MATHEMATICS
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2019, Volume 291, Issue 3, pp. 1337 - 1356
We prove a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue... 
Weighted sum formulas | Bernoulli numbers | 11M32 | Multiple zeta values | Mathematics, general | Mathematics | Multiple zeta-star values | 11B68 | MATHEMATICS
Journal Article
by Xu, Ce
Results in Mathematics, ISSN 1422-6383, 3/2018, Volume 73, Issue 1, pp. 1 - 22
In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated... 
11M40 | restricted sum formula | 33E20 | multiple zeta star value | 40B05 | Mathematics, general | Mathematics | 11M06 | Multiple zeta value | MATHEMATICS | MATHEMATICS, APPLIED | ANALOGS | HARMONIC SUMS | DUALITY | FORMULAS
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 10/2017, Volume 13, Issue 9, pp. 2253 - 2264
... ) . An explicit evaluation of the multiple zeta-star value ζ ⋆ ( { m } n ) is also obtained, as well as some applications to evaluation of multiple zeta values... 
MATHEMATICS | multiple zeta-star value | digamma function | Multiple zeta value | gamma function
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2017, Volume 14, Issue 3, pp. 1 - 13
The purpose of this paper is the presentation of an identity which is closely related to the sum relation involving multiple zeta star values with even arguments. Let $$E^{\star }(m,n,k)$$ E ⋆ ( m , n , k... 
infinite series and products | alternating multiple zeta values | sum formula | 11M32 | Riemann zeta function | Mathematics, general | multiple zeta value | generating functions | Mathematics | 11M06 | 11B68 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 332, Issue 1, pp. 187 - 208
...-)multiple zeta values and the ( q-)multiple zeta-star values. These two classes of values generate the same algebra, but in this paper, we show that the translation map... 
Multiple zeta values | Multiple zeta-star values | Harmonic algebra | q-Series | Q-Series | POLYLOGARITHMS | MATHEMATICS | HARMONIC SERIES | ALGEBRA | SUM
Journal Article
Italian Journal of Pure and Applied Mathematics, ISSN 1126-8042, 02/2018, Issue 39, pp. 710 - 756
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 04/2017, Volume 13, Issue 3, pp. 705 - 716
... ) and for the analogous numbers E ⋆ ( 2 n , k ) defined using multiple zeta-star values of even arguments. 
Multiple zeta values | multiple zeta-star values | symmetric functions | Bernoulli numbers | MATHEMATICS | GENERATING FUNCTION | HARMONIC SERIES | Mathematics - Number Theory
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 08/2019, Volume 15, Issue 7, pp. 1323 - 1348
.... We complement and generalize earlier results. Moreover, we survey properties of certain truncated multiple zeta and zeta star values, pointing out their relation to finite sums of harmonic numbers... 
MATHEMATICS | KANEKO | SYMMETRIC FUNCTIONS | Stirling series | Harmonic numbers | Multiple zeta values | ARAKAWA | MELLIN TRANSFORMS | multiple zeta star values | Arakawa-Kaneko zeta function | SUMS
Journal Article
Ramanujan Journal, ISSN 1382-4090, 06/2010, Volume 22, Issue 2, pp. 153 - 162
.... We give in particular a new expression of the special values of this function at integral points in terms of modified Bell polynomials... 
Euler sums | Multiple zeta-star values | Zeta values | Poly-Bernoulli numbers | MATHEMATICS | VALUES
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 05/2017, Volume 28, Issue 5, p. 1750033
In this paper, the extended double shuffle relations for interpolated multiple zeta values (MZVs) are established... 
Multiple zeta values | multiple zeta-star values | hypergeometric function | interpolated multiple zeta values | MATHEMATICS | FIXED WEIGHT | HARMONIC SERIES | DUALITY | SUM | HEIGHT | DEPTH | STAR VALUES
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 10/2017, Volume 184, Issue 2, pp. 217 - 243
... ^\star (\{2\}_K,1)=2\zeta (2K+1)$$ ζ ⋆ ( { 2 } K , 1 ) = 2 ζ ( 2 K + 1 ) , $$K\in \mathbb {N}$$ K ∈ N . As a corollary of our parametric results, we also prove several sum formulas involving multiple zeta-star values. 
Parametric infinite series | 11M32 | 11M35 | Mathematics, general | Mathematics | Multiple zeta-star values | Sum formula | MATHEMATICS | CYCLIC SUM | VALUES
Journal Article
Monatshefte fur Mathematik, ISSN 0026-9255, 2014, Volume 176, Issue 2, pp. 275 - 291
.... Very recently, Zhao generalized this set of MHS identities to strings with repetitions of the above patterns and, as an application, proved the two-one formula for multiple zeta star values... 
q-Analogues of multiple zeta values | q-Binomial identity | Two-one formulas | Multiple zeta value | Multiple harmonic sum
Journal Article
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