Multiple harmonic series.

  title={Multiple harmonic series.},
  author={M. S. Hoffman},
  journal={Pacific Journal of Mathematics},
  • M. S. Hoffman
  • Published 1992
  • Mathematics
  • Pacific Journal of Mathematics
Explicit Relations of Some Variants of Convoluted Multiple Zeta Values
Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values (MVZs) around 2016. In this paper, we will first establish some explicit formulas involving these values and theirExpand
Explicit relations between multiple zeta values and related variants
  • Ce Xu
  • Computer Science, Mathematics
  • Adv. Appl. Math.
  • 2021
In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods of iterated integral computations of logarithmExpand
Duality of Weighted Sum Formulas of Alternating Multiple $T$-Values
Recently, a new kind of multiple zeta value level two $T({\bf k})$ (which is called multiple $T$-values) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind ofExpand
Explicit Relations between Kaneko--Yamamoto Type Multiple Zeta Values and Related Variants
In this paper we first establish several integral identities. These integrals are of the form \[\int_0^1 x^{an+b} f(x)\,dx\quad (a\in\{1,2\},\ b\in\{-1,-2\})\] where $f(x)$ is a single-variableExpand
An Odd Variant of Euler Sums
For positive integers $p_1,p_2,\ldots,p_k,q$ with $q>1$, we define the Euler $T$-sum $T_{p_1p_2\cdots p_k,q}$ as the sum of those terms of the usual infinite series for the classical Euler sumExpand
Explicit evaluations of sums of sequence tails
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 - {B_n}){x^n},x \in [ - 1,1]}Expand
Renewal sequences and record chains related to multiple zeta sums
For the random interval partition of $[0,1]$ generated by the uniform stick-breaking scheme known as GEM$(1)$, let $u_k$ be the probability that the first $k$ intervals created by the stick-breakingExpand
A study on multiple zeta values from the viewpoint of zeta-functions of root systems
We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions ofExpand
Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems
The shuffle product plays an important role in the study of multiple zeta values (MZVs). This is expressed in terms of multiple integrals, and also as a product in a certain non-commutativeExpand


P(a,b,c) = 2 r~a 2 k~b Σ ι~cr=\ k=\ l=\ Then P(a, b, c) + P(a, c, b) + P(b, c, a) + P(b, a, c)
A classical introduction to modern number theory
This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve. Expand
On the Evaluation of Some Multiple Series
A New Method of Evaluating ζ(2n)