Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 1009 - 1042

In this paper we are interested in Euler-type sums with products of harmonic numbers, Stirling numbers and Bell numbers...

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

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

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

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

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...

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

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

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 present some new relationships...

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

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

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

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

6.
Full Text
New properties of multiple harmonic sums modulo p and p-analogues of Leshchiner’s series

Transactions of the American Mathematical Society, ISSN 0002-9947, 2014, Volume 366, Issue 6, pp. 3131 - 3159

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...

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

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

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

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

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 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...

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

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

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

Multiple zeta values | multiple zeta-star values | symmetric functions | Bernoulli numbers | MATHEMATICS | GENERATING FUNCTION | HARMONIC SERIES | Mathematics - Number Theory

Journal Article

Analysis Mathematica, ISSN 0133-3852, 12/2017, Volume 43, Issue 4, pp. 687 - 707

In this paper, we use Abel’s summation formula to evaluate several quadratic and cubic sums of the form $${F_N}(A,B;x): = \sum\limits_{n = 1}^N {(A - {A_n})(B...

sequence | 11M32 | Analysis | tail | multiple zeta star value (mzsv) | Riemann zeta function | Mathematics | 11M06 | harmonic number | Abel’s summation formula | multiple zeta value (mzv) | MATHEMATICS | MULTIPLE HARMONIC SERIES | Abel's summation formula | VALUES | NONLINEAR EULER SUMS

sequence | 11M32 | Analysis | tail | multiple zeta star value (mzsv) | Riemann zeta function | Mathematics | 11M06 | harmonic number | Abel’s summation formula | multiple zeta value (mzv) | MATHEMATICS | MULTIPLE HARMONIC SERIES | Abel's summation formula | VALUES | NONLINEAR EULER SUMS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 05/2013, Volume 9, Issue 3, pp. 783 - 798

... algebra . The harmonic algebra 1 is closely related to multiple zeta values and multiple zeta-star values in some special case...

harmonic algebra | Multiple zeta values | multiple zeta-star values | MATHEMATICS | Algebra

harmonic algebra | Multiple zeta values | multiple zeta-star values | MATHEMATICS | Algebra

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

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

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 10/2013, Volume 9, p. 061

... of the space spanned by the linear relations realized in our algebra. Key words: multiple harmonic series; q-analogue 2010 Mathematics Subject Classication: 11M32; 33E20...

q-analogue | Multiple harmonic series | multiple harmonic series | Q-ZETA VALUES | PHYSICS, MATHEMATICAL

q-analogue | Multiple harmonic series | multiple harmonic series | Q-ZETA VALUES | PHYSICS, MATHEMATICAL

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2017, Volume 481, pp. 293 - 326

Quasi-shuffle products, introduced by the first author, have been useful in studying multiple zeta values and some of their analogues and generalizations. The...

Quasi-shuffle product | Multiple zeta values | Infinitesimal Hopf algebra | Hopf algebra | MATHEMATICS | MULTIPLE HARMONIC SUMS | ZETA-STAR VALUES | Algebra

Quasi-shuffle product | Multiple zeta values | Infinitesimal Hopf algebra | Hopf algebra | MATHEMATICS | MULTIPLE HARMONIC SUMS | ZETA-STAR VALUES | Algebra

Journal Article

17.
Full Text
New properties of multiple harmonic sums modulo p and p-analogues of Leshchiner's series

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2014, Volume 366, Issue 6, pp. 3131 - 3159

based on a finite identity for partial sums of the zeta-star series.]]>

Integers | Numbers | Prime numbers | Mathematical theorems | Algebra | Discrete mathematics | Harmonic series | Mathematical functions | Mathematical congruence | Number theory | MIXED TATE MOTIVES | POLYNOMIALS | MATHEMATICS | BERNOULLI NUMBERS | IDENTITIES | Multiple harmonic sum | multiple zeta value | ZETA VALUES | Bernoulli number | congruence | CONGRUENCES | FORMULAS

Integers | Numbers | Prime numbers | Mathematical theorems | Algebra | Discrete mathematics | Harmonic series | Mathematical functions | Mathematical congruence | Number theory | MIXED TATE MOTIVES | POLYNOMIALS | MATHEMATICS | BERNOULLI NUMBERS | IDENTITIES | Multiple harmonic sum | multiple zeta value | ZETA VALUES | Bernoulli number | congruence | CONGRUENCES | FORMULAS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 12/2012, Volume 8, Issue 8, pp. 1903 - 1921

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and...

Parametrized sum formula | Multiple polylogarithm | Weighted sum formula | Multiple zeta value | weighted sum formula | MIXED TATE MOTIVES | MATHEMATICS | multiple polylogarithm | HARMONIC SERIES | DUALITY | HEIGHT | parametrized sum formula | STAR VALUES | Mathematics - Number Theory

Parametrized sum formula | Multiple polylogarithm | Weighted sum formula | Multiple zeta value | weighted sum formula | MIXED TATE MOTIVES | MATHEMATICS | multiple polylogarithm | HARMONIC SERIES | DUALITY | HEIGHT | parametrized sum formula | STAR VALUES | Mathematics - Number Theory

Journal Article

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, 01/2020, Volume 43, Issue 1, pp. 847 - 877

...) and x is an element of [-1, 1), define the so-called Euler-type sums Sp(1) p(2)... p(m), p (x), which are the infinite sums whose general term is a product of harmonic numbers of index n, a power of n...

MATHEMATICS | Polylogarithm function | IDENTITIES | Harmonic number | Multiple harmonic sum | Euler sum | Riemann zeta function | Multiple zeta value | EXPLICIT EVALUATION | MULTIPLE ZETA VALUES

MATHEMATICS | Polylogarithm function | IDENTITIES | Harmonic number | Multiple harmonic sum | Euler sum | Riemann zeta function | Multiple zeta value | EXPLICIT EVALUATION | MULTIPLE ZETA VALUES

Journal Article

Journal of number theory, ISSN 0022-314X, 09/2020, Volume 214, pp. 177 - 201

In this paper we consider iterated integral representations of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm...

Multiple zeta values | Borwein-Bradley-Broadhurst's conjectures | Multiple harmonic (star) sums | Multiple polylogarithm functions | Iterated integrals | INTEGRALS | IDENTITY | MATHEMATICS | KANEKO | SERIES | HARMONIC SUMS | ARAKAWA

Multiple zeta values | Borwein-Bradley-Broadhurst's conjectures | Multiple harmonic (star) sums | Multiple polylogarithm functions | Iterated integrals | INTEGRALS | IDENTITY | MATHEMATICS | KANEKO | SERIES | HARMONIC SUMS | ARAKAWA

Journal Article

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