Related papers: Parametric Ap\'{e}ry-type Series and Hurwitz-type …
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…
By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special…
By using the Wilf-Zeilberger method, we prove a novel finite combinatorial identity related to a bivariate generating function for $\zeta(2+r+2s)$ (an extension of a Bailey-Borwein-Bradley Apery-like formula for even zeta values). Such…
We obtain a new proof of Hurwitz's formula for the Hurwitz zeta function $\zeta(s, a)$ beginning with Hermite's formula. The aim is to reveal a nice connection between $\zeta(s, a)$ and a special case of the Lommel function $S_{\mu,…
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.
We give a proof of double shuffle relations for $p$-adic multiple zeta values by developing higher dimensional version of tangential base points and discussing a relationship with two (and one) variable $p$-adic multiple polylogarithms.
Relying on the Hurwitz formula, we find sums of the series over sine and cosine functions through the Hurwitz zeta function. Using another summation formula for these trigonometric series, we find finite sums of some series over the Riemann…
We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…
By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's Ap\'ery-like formulae for odd zeta values. As a…
In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting…
We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
We explain how Gaussian integrals over ensemble of complex matrices with source matrices generate Hurwitz numbers of the most general type, namely, Hurwitz numbers with arbitrary orientable or non-orientable base surface and arbitrary…
In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…
We first survey the known results on functional equations for the double zeta-function of Euler type and its various generalizations. Then we prove two new functional equations for double series of Euler-Hurwitz-Barnes type with complex…
Let $f(t)=\sum_{n=0}^{+\infty}\frac{C_{f,n}}{n!}t^n$ be an analytic function at $0$, and let $C_{f, n}(x)=\sum_{k=0}^{n}\binom{n}{k}C_{f,k} x^{n-k}$ be the sequence of Appell polynomials, referred to as $\textit{C-polynomials associated to…
We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums 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 recall a proof of Euler's identity $\sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}$ involving the evaluation of a double integral. We extend the method to find Hurwitz Zeta series of the form $S(k,a)=\sum_{n \in \mathbb{Z}}…
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…