相关论文: On the Sum Formula for Multiple q-Zeta Values

Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of…

Hirose, Saito, and the author established the weighted sum formula for finite multiple zeta(-star) values. In this paper, we present its alternative proof. The proof is also valid for symmetric multiple zeta(-star) values.

We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the…

In this survey article, we discuss the algebraic structure of q-analogues of multiple zeta values, which are closely related to derivatives of Eisenstein series. Moreover, we introduce the formal double Eisenstein space, which generalizes…

In this paper we discuss three types of the mean values of the Euler double zeta function. In order to get results we introduce three approximate formulas for this function.

In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…

For positive integers $i_1,...,i_k$ with $i_1 > 1$, we define the multiple $t$-value $t(i_1,...,i_k)$ as the sum of those terms in the usual infinite series for the multiple zeta value $\zeta(i_1,...,i_k)$ with odd denominators. Like the…

Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle…

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 of alternating version of multiple $T$-values, and…

We introduce the balanced multiple q-zeta values. They give a new model for multiple q-zeta values, whose product formula combines the shuffle and stuffle product for multiple zeta values in a natural way. Moreover, the balanced multiple…

Recently, the higher-order q-Euler polynomials and multiple q-Euler zeta functions are introduced by T. Kim ([8, 9]). In this paper, we investigate some symmetric properties of the multiple q-Euler zeta function and derive various…

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…

One of the most interesting formulas for multiple zeta values is the sum formula proved by Granville and Zagier independently in 1990s. Many variations and generalizations of it have been found since then. In this paper, we will provide a…

In this paper, we construct generating functions of alternating sums for the Arakawa-Kaneko zeta values. From the expressions, we show alternating sum formulas for them. Based on these results, we apply the same method to other zeta values.

We introduce an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. The double shuffle relations are formulated in our framework. They contain a q-analogue of…

Multiple zeta values (MZVs) are real numbers which are defined by certain multiple series. Recently, many people have researched for relations among them and many relations are well known. In this paper, we get a new relation among them…

Quasi-shuffle algebras have been a useful tool in studying multiple zeta values and related quantities, including multiple polylogarithms, finite multiple harmonic sums, and q-multiple zeta values. Here we show that two ideas previously…

Recently, Dil and Boyadzhiev \cite{AD2015} proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence $\left( {{{\left\{ 0 \right\}}_r},1} \right)$. In this paper we show that the sums of multiple…

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…