The Rocky Mountain journal of mathematics, ISSN 0035-7596, 04/2020, Volume 50, Issue 2, pp. 551 - 558

We evaluate the multiple zeta value zeta(1, {2}(n+1)) or its dual zeta({2}(n),( )3). When n is even, along with stuffle relations already available, it is...

modified Bell polynomial | MATHEMATICS | multiple zeta-star value | multiple zeta value | Bernoulli polynomial

modified Bell polynomial | MATHEMATICS | multiple zeta-star value | multiple zeta value | Bernoulli polynomial

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 11/2018, Volume 14, Issue 10, pp. 2617 - 2630

For positive integers m , n , k with m ≥ 2 and ⌈ n / 2 ⌉ ≤ k ≤ n , let E { m } ( m , n , k ) be the sum of multiple zeta values of depth k and weight m n with...

modified Bell polynomial | generating function | stuffle relation | Multiple zeta value | MATHEMATICS | SERIES | stale relation

modified Bell polynomial | generating function | stuffle relation | Multiple zeta value | MATHEMATICS | SERIES | stale relation

Journal Article

10/2018

In this paper, we investigate the Euler sums $$ G_{n+2}(p,q)=\sum_{1\leq k_1 Mathematics - Number Theory

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2018, Volume 188, pp. 247 - 262

In this paper, we are going to evaluate a family {Ep(2m,n,k)|p∈Z} of sums of multiple zeta values with even arguments and polynomial weights defined...

Multiple zeta values | Weighted sum formula | Multiple zeta-star value | MATHEMATICS

Multiple zeta values | Weighted sum formula | Multiple zeta-star value | MATHEMATICS

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

MATHEMATICS | multiple zeta-star value | digamma function | Multiple zeta value | gamma function

Journal Article

6.
Full Text
Sum formulas of multiple zeta values with arguments multiples of a common positive integer

Journal of Number Theory, ISSN 0022-314X, 08/2017, Volume 177, pp. 479 - 496

For k≤n, let E(m,n,k) be the sum of all multiple zeta values of depth k and weight mn with arguments multiples of m≥2. More precisely,...

Multiple zeta values | Multiple zeta-star values | MATHEMATICS

Multiple zeta values | Multiple zeta-star values | MATHEMATICS

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2017, Volume 47, Issue 7, pp. 2107 - 2131

In this paper, we build some variations of multiple zeta values and investigate their relations. Among other things, we prove that Sigma(|alpha| = m+r 1 <= k1...

Restricted sum formula | Duality theorem | Multiple zeta value | Sum formula | MATHEMATICS | restricted sum formula | sum formula | duality theorem

Restricted sum formula | Duality theorem | Multiple zeta value | Sum formula | MATHEMATICS | restricted sum formula | sum formula | duality theorem

Journal Article

Journal of Number Theory, ISSN 0022-314X, 09/2016, Volume 166, pp. 452 - 472

Multiple zeta values or r-ford Euler sums are defined by where α , α , . . ., α are positive integers and α ≥2 for the sake of convergence. Let |α|=α +α +⋯+α...

Secondary | Restricted sum formula | Duality theorem | Multiple zeta value | Primary | Sum formula

Secondary | Restricted sum formula | Duality theorem | Multiple zeta value | Primary | Sum formula

Journal Article

08/2016

For $k\leq n$, let $E(mn,k)$ be the sum of all multiple zeta values of depth $k$ and weight $mn$ with arguments are multiples of $m\geq 2$. More precisely,...

Mathematics - Number Theory

Mathematics - Number Theory

Journal Article

07/2016

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality...

Mathematics - Number Theory

Mathematics - Number Theory

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2016, Volume 164, pp. 208 - 222

The duality theorem and sum formula [8] are undoubtedly the crucial relations among multiple zeta values. They can be expressed as ζ({1}p,q+2)=ζ({1}q,p+2)...

Multiple zeta values | Drinfel'd integrals | Sum formula | Secondary | Primary | MATHEMATICS

Multiple zeta values | Drinfel'd integrals | Sum formula | Secondary | Primary | MATHEMATICS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 02/2016, Volume 12, Issue 1, pp. 15 - 25

In this paper, we extend the Euler decomposition theorem to a much more general form of the decomposition of the product of n multiple zeta values of height...

Multiple zeta value | Euler decomposition theorem | MATHEMATICS | SUM FORMULA

Multiple zeta value | Euler decomposition theorem | MATHEMATICS | SUM FORMULA

Journal Article

Journal of Number Theory, ISSN 0022-314X, 01/2016, Volume 158, pp. 33 - 53

Multiple zeta values or r-ford Euler sums are defined byζ(α1,α2,. .,αr)=∑1≤n1 Multiple zeta values | Duality theorems | Secondary | Sum formulas | Primary | MATHEMATICS

Journal Article

Journal of combinatorics and number theory, ISSN 1942-5600, 05/2015, Volume 7, Issue 2, p. 111

The shuffle product of two multiple zeta values of weight m and n will produce ... multiple zeta values of weight m+n. The well-known Euler decomposition...

Eulers equations | Mathematics | Combinatorics | Number theory

Eulers equations | Mathematics | Combinatorics | Number theory

Journal Article

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 0025-5858, 4/2015, Volume 85, Issue 1, pp. 23 - 41

...Abh. Math. Semin. Univ. Hambg. (2015) 85:23–41 DOI 10.1007/s12188-015-0105-2 Double weighted sum formulas of multiple zeta values Minking Eie · Wen-Chin Liaw...

33E99 | Weighted sum formula | Multiple zeta values | Mathematics | Topology | Geometry | Algebra | Secondary 11M99 | 40B05 | Mathematics, general | Number Theory | Differential Geometry | Drinfeld integral | Shuffle product | Primary 40A25 | MATHEMATICS

33E99 | Weighted sum formula | Multiple zeta values | Mathematics | Topology | Geometry | Algebra | Secondary 11M99 | 40B05 | Mathematics, general | Number Theory | Differential Geometry | Drinfeld integral | Shuffle product | Primary 40A25 | MATHEMATICS

Journal Article

Journal of Combinatorics and Number Theory, ISSN 1942-5600, 01/2015, Volume 7, Issue 2, pp. 111 - 111

The shuffle product of two multiple zeta values of weight m and n will produce ... multiple zeta values of weight m+n. The well-known Euler decomposition...

Permutations | Pascal (programming language) | Theorems | Decomposition | Number theory | Combinatorial analysis | Counting | Sums

Permutations | Pascal (programming language) | Theorems | Decomposition | Number theory | Combinatorial analysis | Counting | Sums

Journal Article

Journal of Number Theory, ISSN 0022-314X, 05/2015, Volume 150, pp. 1 - 20

The classical Euler decomposition theorem expresses a product of two Riemann zeta values in terms of double Euler sums. Also, the sum formula expresses a...

Multiple zeta value | Euler decomposition theorem | MATHEMATICS

Multiple zeta value | Euler decomposition theorem | MATHEMATICS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2015, Volume 147, pp. 749 - 765

The classical Euler decomposition theorem expressed a product of two Riemann zeta values in terms of double Euler sums. It can also be obtained from the...

Multiple zeta values | Shuffle product | Secondary | Primary | MATHEMATICS

Multiple zeta values | Shuffle product | Secondary | Primary | MATHEMATICS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 08/2013, Volume 133, Issue 8, pp. 2475 - 2495

The classical Euler decomposition theorem expressed a product of two Riemann zeta values in terms of double Euler sums. Such kind of decomposition theorem are...

Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA

Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 08/2013, Volume 9, Issue 5, pp. 1185 - 1198

In this paper, we compute shuffle relations from multiple zeta values of the form ζ({1}m-1, n+1) or sums of multiple zeta values of fixed weight and depth....

weighted sum formula | shuffle relation | sum formula | Multiple zeta value | MATHEMATICS | HARMONIC SERIES

weighted sum formula | shuffle relation | sum formula | Multiple zeta value | MATHEMATICS | HARMONIC SERIES

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.