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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. We give an... 
Multiple zeta values | Two-one conjecture | Multiple zeta-star values | Cyclic sum formula | Sum formula | MATHEMATICS
Journal Article
by Xu, Ce
Journal of Number Theory, ISSN 0022-314X, 08/2017, Volume 177, pp. 443 - 478
In this paper, we establish some expressions of series involving harmonic numbers and Stirling numbers of the first kind in terms of multiple zeta values, and... 
Multiple star harmonic number | Euler sum | Multiple zeta star value | Multiple zeta value | Multiple harmonic number | INTEGRALS | MATHEMATICS | SERIES | NUMBERS | DUALITY | FORMULAS | RIEMANN ZETA | Mathematics - Number Theory
Journal Article
Advances in Mathematics, ISSN 0001-8708, 07/2018, Volume 333, pp. 570 - 619
We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler–Zagier type combinatorially.... 
Schur functions | Multiple zeta functions | Quasi-symmetric functions | Jacobi–Trudi formula | MATHEMATICS | Jacobi-Trudi formula | STAR VALUES
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 332, Issue 1, pp. 187 - 208
We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the ( q-)multiple zeta values and the ( q-)multiple... 
Multiple zeta values | Multiple zeta-star values | Harmonic algebra | q-Series | Q-Series | POLYLOGARITHMS | MATHEMATICS | HARMONIC SERIES | ALGEBRA | SUM
Journal Article
COMPOSITIO MATHEMATICA, ISSN 0010-437X, 12/2018, Volume 154, Issue 12, pp. 2701 - 2721
We study the values of finite multiple harmonic q-series at a primitive root of unity and show that these specialize to the finite multiple zeta value (FMZV)... 
MATHEMATICS | finite multiple harmonic q-series | symmetric multiple zeta (star) values | finite multiple zeta (star) values | Kaneko-Zagier conjecture | multiple zeta (star) values | SUM FORMULA | Mathematics - Number Theory
Journal Article
Journal of the Australian Mathematical Society, ISSN 1446-7887, 06/2018, Volume 104, Issue 3, pp. 289 - 307
Inspired by the recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki, we combine interpolated multiple zeta values and Schur multiple zeta values into one... 
Schur functions | interpolated multiple zeta values | multiple zeta values | Jacobi-Trudi formula | MATHEMATICS | STAR VALUES
Journal Article
Ramanujan Journal, ISSN 1382-4090, 06/2010, Volume 22, Issue 2, pp. 153 - 162
We present a very natural generalization of the Arakawa-Kaneko zeta function introduced ten years ago by T. Arakawa and M. Kaneko. We give in particular a new... 
Euler sums | Multiple zeta-star values | Zeta values | Poly-Bernoulli numbers | MATHEMATICS | VALUES
Journal Article
Taiwanese Journal of Mathematics, ISSN 1027-5487, 6/2018, Volume 22, Issue 3, pp. 529 - 543
Using the combinatorial descriptions of stuffle product, we obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star... 
Multiple zeta values | Stuffle product | Multiple zeta-star values | MATHEMATICS | DECOMPOSITION | multiple zeta-star values | Stuffel product | multiple zeta values | SHUFFLE PRODUCT
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 04/2017, Volume 13, Issue 3, pp. 705 - 716
For k ≤ n , let E ( 2 n , k ) be the sum of all multiple zeta values with even arguments whose weight is 2 n and whose depth is k . Of course E ( 2 n , 1 ) is... 
Multiple zeta values | multiple zeta-star values | symmetric functions | Bernoulli numbers | MATHEMATICS | GENERATING FUNCTION | HARMONIC SERIES | Mathematics - Number Theory
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. As an application, Hoffman’s relations for... 
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
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... 
Weighted sum formulas | Bernoulli numbers | 11M32 | Multiple zeta values | Mathematics, general | Mathematics | Multiple zeta-star values | 11B68 | MATHEMATICS
Journal Article
Monatshefte fur Mathematik, ISSN 0026-9255, 2014, Volume 176, Issue 2, pp. 275 - 291
Recently, the present authors jointly with Tauraso found a family of binomial identities for multiple harmonic sums (MHS) on strings (\2\.sup.a,c,\2\.sup.b)... 
q-Analogues of multiple zeta values | q-Binomial identity | Two-one formulas | Multiple zeta value | Multiple harmonic sum
Journal Article
Journal of Number Theory, ISSN 0022-314X, 09/2012, Volume 132, Issue 9, pp. 1984 - 2002
The Bowman–Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed number of twos between 3,1,…,3,1 add up to a... 
Bowman–Bradley theorem | Harmonic algebra | Multiple zeta value | Multiple zeta-star value | Bowman-Bradley theorem | MATHEMATICS | HARMONIC SERIES | ALGEBRA | Insurance industry | Algebra | Universities and colleges
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2016, Volume 68, Issue 4, pp. 1669 - 1694
In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results... 
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
International Journal of Number Theory, ISSN 1793-0421, 10/2017, Volume 13, Issue 9, pp. 2253 - 2264
For a real number β ≠ 0 and positive integers m and n with m ≥ 2 , we evaluate the sum of multiple zeta values ∑ k = 1 n ∑ | α | = n β α 1 β α 2 ⋯ β α k ζ ( m... 
MATHEMATICS | multiple zeta-star value | digamma function | Multiple zeta value | gamma function
Journal Article
Communications in Number Theory and Physics, ISSN 1931-4523, 2016, Volume 10, Issue 4, pp. 805 - 832
In recent years, there has been intensive research on the Q-linear relations between multiple zeta (star) values. In this paper, we prove many families of... 
Euler sums | Multiple zeta values | Multiple harmonic sums | Multiple zeta star values | POLYLOGARITHMS | MATHEMATICS | MATHEMATICS, APPLIED | multiple harmonic sums | SERIES | multiple zeta values | multiple zeta star values | PHYSICS, MATHEMATICAL | MOTIVES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2016, Volume 298, pp. 254 - 285
Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a... 
Rota–Baxter algebra | Double shuffle relations | Hoffman–Ohno relation | Infinitesimal bialgebra | q-Analogues | Derivation relations | Multiple zeta values | Duality | Hopf algebra | Hoffman-Ohno relation | Rota-Baxter algebra | Q-Analogues | MATHEMATICS | Algebra | Singers | Mathematics - Number Theory
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2018, Volume 462, Issue 1, pp. 777 - 800
In this work, we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double Euler... 
Multiple zeta values | Multiple zeta star values | Hypergeometric identities | Double Euler sums | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | ZETA VALUES ZETA(2,...,2,3,2,...,2) | PROOF | MULTIPLE
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2018, Volume 290, Issue 3, pp. 1173 - 1197
We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young... 
Hypergeometric functions | 11M41 | Jacobi–Trudi formula | Hankel determinants | Multiple zeta values | Schur functions | 05E05 | Mathematics, general | Mathematics | 33C05 | MATHEMATICS | Jacobi-Trudi formula
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 08/2019, Volume 15, Issue 7, pp. 1323 - 1348
We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values... 
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
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