Related papers: A note on the Voigt profile function
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…
The Voigt profile is one of the most used special function in optical spectroscopy. In particle physics a version of this profile which originates from relativistic Breit-Wigner resonance distribution often appears, however, in the…
The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing…
The Fox $H$-function is a special function which is defined via the Mellin-Barnes integrals and produces, as particular cases, Wright generalized hypergeometric functions, MacRobert's $E$-functions and Meijer $G$-functions, to name but few.…
The Voigt-Hjerting function is fundamental in order to correctly model the profiles of absorption lines imprinted in the spectra of bright background sources by intervening absorbing systems. In this work we present a simple analytic…
Evaluation of the Voigt function, a convolution of a Lorentzian and a Gaussian profile, is essential in various fields such as spectroscopy, atmospheric science, and astrophysics. Efficient computation of the function is crucial, especially…
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…
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
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 Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by K.…
In this paper we find several new properties of a class of Fox's H functions which we call delta neutral. In particular, we find an expansion in the neighborhood of finite nonzero singularity and give new Mellin transform formulas under a…
In this paper we present a generalization of the Fox H-function called Fox-Barnes J-function. Like the Fox H-function, it is defined as a contour integral in the complex plane, but instead of an integrand given by a ratio of products of…
Powder X-ray Diffraction (PXRD) and Pair Distribution Function (PDF) analysis are well-established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In PXRD…
The Sersic model has become the standard to parametrize the surface brightness distribution of early-type galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sersic surface brightness profile to a…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of…
We evaluate an adaptive gaussian quadrature integration scheme that will be suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for "full non-LTE" radiation…
The Voigt profile is important for spectroscopy, astrophysics, and many other fields of physics, but is notoriously difficult to compute. McLean et al. [J. Electron Spectrosc. & Relat. Phenom., 1994] have proposed an approximation using a…
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this…