Related papers: Having Fun with Lambert W(x) Function
The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the…
A generalization of the Wigner function for the case of a free particle with the ``relativistic'' Hamiltonian $\sqrt{{\bf p}^2+m^2}$ is given.
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are calculated. These derivatives can be expressed in the form of infinite sums of quotients of…
We present the main improvements and new features in version $\texttt{2.0}$ of the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid…
We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…
A basic concept to calculate physical features of non-ideal plasmas, such as optical properties, is the spectral function which is linked to the self-energy. We calculate the spectral function for a non-relativistic hydrogen plasma in…
The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to…
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions…
The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives…
The expansion of Kummer's hypergeometric function as a series of incomplete Gamma functions is discussed, for real values of the parameters and of the variable. The error performed approximating the Kummer function with a finite sum of…
We present a new approach to examine transient dynamics in a class of non-autonomous delay differential equations. Exact solutions for these equations are obtained using the Lambert W function alongside an appropriately chosen initial…
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.
We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for the…
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson…