8 Results Found

We investigate the linear arrangement of Euler harmonic sums that may be expressed in closed form in terms of special functions such as the classical Riemann zeta function and the Dirichlet eta function. Particular emphasis is given to Euler harmonic...

A very recent article delved into and expanded the four parametric linear Euler sums, revealing that two well-established subjects—Euler sums and series involving the zeta functions—display particular correlations. In this study, we prese...

We develop a number of new identities for linear Euler harmonic number sums with multiple argument. Some new examples of even weight linear Euler harmonic sum identities are given.

In this paper, we will study finite multiple T-values (MTVs) and their alternating versions, which are level two and level four variations of finite multiple zeta values, respectively. We will first provide some structural results for level two finit...

We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby produci...

We define a Euler characteristic $\chi (X,G)$ for a finite cell complex X with a finite group G acting cellularly on it. Then, each $K_i\left(X\right)$ (a complex vector space with basis the i-cells of X) is a representation of G, and we define $\chi (X,G)$ to be the...

In recent years, a variety of multiple zeta values (MZVs) variants have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include Hoffman’s multi...

We study the half-integer family $F(n,p)={}_{3}F_2\left(-\frac{2n+1}{2},1,\frac{2p-1}{2};\frac{2n+5}{2},\frac{2p+1}{2};1\right).$ Although this family belongs to the Karlsson–Minton class of ${}_{3}F_2\left(1\right)$ series with negative integral parameter differences, the most directly relevant symmetric f...