We present a number of results about (finite) multiple harmonic sums modulo a prime, which
provide interesting parallels to known results about multiple zeta values (ie infinite multiple …

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 …

In this paper, firstly, we aim to investigate analytic continuations of altogether four types of
parametric linear Euler sums, by using the Euler-Maclaurin summation formula and the …

We review some basic properties of multiple zeta values, in particular the theory of
regularization and its connection to an identity between certain integral and series …

In 1920, PA MacMahon generalized the (classical) notion of divisor sums by relating it to the
theory of partitions of integers. In this paper, we extend the idea of MacMahon. In doing so …

Flajolet and Salvy pointed out that every Euler sum is a Q-linear combination of multiple zeta
values. However, in the literature, there is no formula completely revealing this relation. In …

Abstract Recently Alzer and Choi proposed and studied a set of the four Euler sums being
linear with parameters. These sums are parametric extensions of Flajolet and Salvy's four …

Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the
iterated integral expressions of multiple zeta values become discretized. In this paper, we …

Recently, several people study finite multiple zeta values (FMZVs) and finite polylogarithms
(FPs). In this paper, we introduce finite multiple polylogarithms (FMPs), which are natural …

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 of Hessami Pilehrood …