Related papers: Generalized Polylogarithms in Maple
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values, with rational coefficients.
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…
In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short $S$-sums) arise. They are characterized by…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
In the last decade major steps towards an algorithmic treatment of orthogonal polynomials and special functions (OP & SF) have been made, notably Zeilberger's brilliant extension of Gosper's algorithm on algorithmic definite hypergeometric…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
This paper investigates the generalized beta-logarithmic matrix function (GBLMF),which combines the extended beta matrix function and the logarithmic mean. The study establishes essential properties of this function, including functional…
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
We construct polylogarithms on families of pointed Riemann surfaces of any genus which describe monodromies of meromorphic connections with simple poles. Furthermore, we show that the polylogaritms are computable as power series in…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms,…
In this paper, we introduce the interpolated multiple $t$-values of general level and represent a generating function for sums of interpolated multiple $t$-values of general level with fixed weight, depth, and height in terms of a…
In this paper, we study some properties of multivariate gamma function and zonal polynomials.
In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers
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…
Machine learning potentials (MLPs) developed from extensive datasets constructed from density functional theory (DFT) calculations have become increasingly appealing for many researchers. This paper presents a framework of polynomial-based…