Related papers: Having Fun with Lambert W(x) Function
The Pierre Auger Observatory is designed to unveil the nature and the origins of the highest energy cosmic rays. The large and geographically dispersed collaboration of physicists and the wide-ranging collection of simulation and…
The Pierre Auger Observatory is designed to unveil the nature and the origins of the highest energy cosmic rays. The large and geographically dispersed collaboration of physicists and the wide-ranging collection of simulation and…
This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…
A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field…
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and…
Theoretical calculations Beyond the Standard Model (BSM) constitute a challenge for high energy physicists, but are necessary when searching for New Physics. The predictions of a BSM scenario need to be compared with experimental data and…
We present a MATLAB function for the numerical evaluation of the Faddeyeva function w(z). The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs…
The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical…
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…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
In 1975, Don Zagier obtained a new version of the Kronecker limit formula for a real quadratic field which involved an interesting function $F(x)$ which is now known as the \emph{Herglotz function}. As demonstrated by Zagier, and very…
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-analogue of the Schur function $s_\lambda(\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial…
We study a class of integrable nonhomogeneous Lotka-Volterra systems whose quadratic terms are defined by an antisymmetric matrix and whose linear terms consist of three blocks. We provide the Poisson algebra of their Darboux polynomials,…
In this paper, four parameters Wright function is considered. Certain geometric properties such as starlikeness, convexity, uniform convexity and close-to-convexity are discussed for this function. Further, certain geometric properties of…
The familiar tools of Fourier analysis and Fisher matrices are applied to derive the uncertainties on photometric, astrometric, and weak-lensing measurements of stars and galaxies in real astronomical images. Many effects or functions that…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…