Related papers: A note on the Voigt profile function
In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic…
In the framework of statistical optics, a Wigner function represents partially coherent radiation. A Gaussian Wigner function, which is an equivalent representation of the more commonly used Gaussian Schell-model cross-spectral density, may…
The present work proposes analytical solutions for the integral of bivariate Fox H-function in combination with algebraic, exponential, and complementary error functions. In addition, the work also presents the derivative identities with…
To go beyond Gaussian approximation to the Hohenberg-Kohn free energy playing the key role in the density functional theory (DFT), the density functional \textit{integral} representation would be relevant, because field theoretical approach…
The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…
Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…
The S\'ersic model is the de facto standard to describe the surface brightness distribution of hot stellar systems. An important inconvenience of this analytical model is that the corresponding luminosity density and associated properties…
New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…
Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three distinct velocity distributions,…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit…
Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudo-scalar mesons, belonging both to the light quarks sector and to the one of…
We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the…
Expressions describing the vortex beams, which are generated in a process of Fresnel diffraction of a Gaussian beam, incident out of waist on a fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer…
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…