Related papers: The package HarmonicSums: Computer Algebra and Ana…
We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, $\sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ...…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…
The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically is computed by first discretizing the problem and then…
Harmonic numbers arise from the truncation of the harmonic series. The $n^\text{th}$ harmonic number is the sum of the reciprocals of each positive integer up to $n$. In addition to briefly introducing the properties of harmonic numbers, we…
We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
This paper contains a number of series whose coefficients are products of central binomial coefficients & harmonic numbers. An elegant sum involving $\zeta(2)$ and two other nice sums appear in the last section.
A Mathematica package for color summed calculations in QCD (SU(Nc)) is presented. Color contractions of any color amplitude appearing in QCD may be performed, and the package uses a syntax which is very similar to how color structure is…
Two classes of infinite series involving harmonic numbers and the binomial coefficient $C(3n,n)$ are evaluated in closed form using integrals. Several remarkable integral values and difficult series identities are stated as special cases of…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The Python package ComCH is a lightweight specialized computer algebra system that provides models for well known objects, the surjection and Barratt-Eccles operads, parameterizing the product structure of algebras that are commutative in a…
We propose a harmonic surface mapping algorithm (HSMA) for electrostatic pairwise sums of an infinite number of image charges. The images are induced by point sources within a box due to a specific boundary condition which can be…
The paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with introduction of new concepts like the smoothing operator and semi-harmonic…