Related papers: A C++ Incarnation of Zernike Circle Functions
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based…
Generalized log-sine functions appear in higher order epsilon-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with…
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…
We review the dimensional check problem of the high-level programming languages, discuss the existing solutions, and come up with a new solution suited for scientific and engineering computations. Then, we introduce Univec, our C++ library…
A generalization of the Zernike circle polynomials for expansion of functions vanishing outside the unit disk is given. These generalized Zernike functions have the form Zm,{\alpha} n ({\rho}, \vartheta) = Rm,{\alpha} n ({\rho})…
RiemCirc is a C++ program which allocates points inside the unit circle for numerical quadrature on the circle, aiming at homogeneous equidistant distribution. The weights of the quadrature rule are computed by the area of the tiles that…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
This short note presents the Lambert W(x) function and its possible application in the framework of physics related to the Pierre Auger Observatory. The actual numerical implementation in C++ consists of Halley's and Fritsch's iteration…
Several quantities related to the Zernike circle polynomials admit an expression as an infinite integral involving the product of two or three Bessel functions. In this paper these integrals are identified and evaluated explicitly for the…
The qft++ package is a library of C++ classes that facilitate numerical (not algebraic) quantum field theory calculations. Mathematical objects such as matrices, tensors, Dirac spinors, polarization and orbital angular momentum tensors,…
This paper provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element…
Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic…
I present a lightweight C++ library for the evaluation of classical polylogarithms Li_n and the special function Li_{22} for arbitrary complex arguments. The evaluation is possible in arbitrary precision arithmetic and features also an…
The \textsc{Greens} library is presented which provides a set of C++ procedures for the computation of the (radial) Coulomb wave and Green's functions. Both, the nonrelativistic as well as relativistic representations of these functions are…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order. Due to the nature of the Zernike…
This paper presents a systematic study for analytic aspects of Fourier-Zernike series of convolutions of functions supported on disks. We then investigate different aspects of the presented theory in the cases of zero-padded functions.
Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of…