Related papers: Mixed Berndt-Type Integrals and Generalized Barnes…
We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding suitable rigorous meaning of the values of multiple zeta-functions at…
We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
The Watson-Harkins sum involving the product of the cosine and cosecant functions is extended to derive the finite sum of generalized Hurwitz-Lerch Zeta functions is derived in terms of the Hurwitz-Lerch Zeta function. A transformation…
In this work, we begin to uncover the architecture of the general family of zeta functions and multiple zeta values as they appear in the theory of integrable systems and conformal field theory. One of the key steps in this process is to…
We introduce and survey results on two families of zeta functions connected to the multiplicative and additive theories of integer partitions. In the case of the multiplicative theory, we provide specialization formulas and results on the…
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…
We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…
In this Ph.D. thesis, written under the direction of D.B. Zagier and R.W. Bruggeman, we study the mock theta functions, that were introduced by Ramanujan. We show how they can be interpreted in the theory of (real-analytic) modular forms.…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
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…
In this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler's multiple zeta values.…
By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also…
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta. These derivations are then…
A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical…
This article deals with three types of mutually inverse series relating Ferrers and associated Legendre functions of arbitrary complex indexes and orders established on the base of integral representations by using a number of generating…
We present a new systematic method for evaluating generalized log-sine integrals in terms of polylogarithms. Our approach is based on an identity connecting ordinary generating functions of polylogarithms to integrals involving the sine…