Related papers: On functional equations of finite multiple polylog…
We introduce a hypergoemetirc series with two complex variables, which generalizes Appell's, Lauricella's and Kemp\'e de F\'eriet's hypergeometric series, and study the system of differential equations that it satisfies. We determine the…
The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard fundamentals will be given. For some…
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin…
In this article, we introduce an algebraic setup of non-strict multiple zeta values (NMZVs, for short) and prove some relations of NMZVs, which are analogous to Hoffman's relations of multiple zeta values, by using this algebraic setup of…
This paper presents a new method to solve functional equations of multivariate generating functions, such as $$F(r,s)=e(r,s)+xf(r,s)F(1,1)+xg(r,s)F(qr,1)+xh(r,s)F(qr,qs),$$ giving a formula for $F(r,s)$ in terms of a sum over finite…
Integral representations for continuous polynomial local functionals on convex functions are established in terms of a finite family of polynomials. This result is obtained by approximation from a classification of the dense subspace of…
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…
We address a class of definite integrals known as Berndt-type integrals, highlighting their role as specialized instances within the integral representation framework of the Barnes-zeta function. Building upon the foundational insights of…
We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions…
We prove a new linear relation for multiple zeta values. This is a natural generalization of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.
In the former part of this paper, we give functional equations for Barnes multiple zeta-functions and consider some relevant results. In particular, we show that Ramanujan's classical formula for the Riemann zeta values can be derived from…
We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic…
The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the…
Take complex numbers $a_j,b_j$, $(j=0,1,2)$ such that $c\neq0$ and {\rm rank} ( {ccc} a_{0} & a_{1} & a_{2} b_{0} & b_{1} & b_{2} )=2. We show that if the following functional equation of Fermat type…
We consider the three finite free convolutions for polynomials studied in a recent paper by Marcus, Spielman, and Srivastava. Each can be described either by direct explicit formulae or in terms of operations on randomly rotated matrices.…
We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of those functional relations is given by the symmetry with…
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of $\mathbb{N}$ where each integer is included independently with probability…
We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at non-positive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as…
In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…
We recall the relation between Zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of Zeta…