Related papers: Numerical Implementation of Harmonic Polylogarithm…
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite…
We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as…
We describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogoliubov calculations with Skyrme-forces and zero-range pairing interaction using Harmonic-Oscillator and/or Transformed Harmonic-Oscillator states. The…
We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the…
One- and two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in calculations of multi-loop integrals. We discuss them in the context of analytical solutions for two-loop master integrals in the case of massive Bhabha scattering…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
The FORTRAN code POLRAD 2.0 for radiative correction calculation in inclusive and semi-inclusive deep inelastic scattering of polarized leptons by polarized nucleons and nuclei is described. Its theoretical basis, structure and algorithms…
We present explicit formulas for the following family of parametric binomial sums involving harmonic numbers for $p=0,1,2$ and $|t|\leq1$. $$ \sum_{k=1}^{\infty}\frac{H_{k-1}t^k}{k^p\binom{n+k}{k}}\quad \mbox{and}\quad…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
In this paper some algorithms will be presented which can be used for the calculation of zeros of polynomials and eigenvalues of polynomial matrices with a multiplicity larger than one. The numerical values calculated with MATLAB are used…
Extraction of harmonics of a given order from real trigonometric polynomials (signals) is one of the main problems in harmonic analysis. It has many applications in physics, radio and electrical engineering, in particular, in filtration of…
Feynman integrals appropriately generalized are $\mathsf A$-hypergeometric functions. Among the properties of $\mathsf A$-hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions…
This article presents numerical methods in order to solve problems of tolerance analysis. A geometric specification, a contact specification and a functional requirement can be respectively characterized by a finite set of geometric…
Accurate yet efficient computation of the Voigt and complex error function is a challenge since decades in astrophysics and other areas of physics. Rational approximations have attracted considerable attention and are used in many codes,…
An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L^{(\alpha)}_n(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic…
Let $w$ be an unbounded radial weight on the complex plane. We study the following approximation problem: find a proper holomorphic map $f: \mathbb{C}\to\mathbb{C}^n$ such that $|f|$ is equivalent to $w$. We give several characterizations…
We consider the problem of evaluation of the weight enumerator of a binary linear code. We show that the exact evaluation is hard for polynomial hierarchy. More exactly, if WE is an oracle answering the solution of the evaluation problem…
In this paper, we introduce Jacobi polynomial generalizations of several classical invariants in coding theory over finite fields, specifically, the higher and extended weight enumerators, and we establish explicit correspondences between…