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The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
Precise nuclear reaction rates are needed for a detailed description of the production of elements in primordial nucleosynthesis and during the hydrostatic burning of stars to constrain the astrophysical models. The relevant reactions are…
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…
We describe a new approach to the notion of general hypergeometric functions
In this paper, modified gamma and beta functions containing generalized M-series in their kernel are defined. Also, modified Gauss and confluent hypergeometric functions are defined using the modified beta function. Then, some properties of…
The theory of the nuclear energy-density functional is used to provide a unified and thermodynamically consistent treatment of all regions of cold non-accreting neutron stars. In order to assess the impact of our lack of complete knowledge…
As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. In this paper mathematical/statistical techniques for deriving…
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…
Astrophysical gamma-ray spectroscopy is an invaluable tool for studying nuclear astrophysics, supernova structure, recent star formation in the Milky Way and mixing of nucleosynthesis products in the interstellar medium. After a short,…
In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been…
We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…
Studies in nuclear astrophysics have long been associated with long runs at small accelerators, measuring ever-decreasing cross sections as one approached (but rarely reached) the energy of reactions in stars. But in recent years pioneering…
This is an overview over the prediction of astrophysical reaction rates in the statistical model, with special emphasis on the parametrization of optical alpha+nucleus potentials.
We have recently developed a set of equations of state based on the nuclear energy density functional theory providing a unified description of the different regions constituting the interior of neutron stars and magnetars. The nuclear…
The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when…
Today the applications of nuclear physics span a very broad range of topics and fields. This review discusses a number of aspects of these applications, including selected topics and concepts in nuclear reactor physics, nuclear fusion,…
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field $\mathbb{R}^{*}\supset\mathbb{R}$ that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…