Related papers: Inverse Laplace transform based on Widder's method…
We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an…
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their…
Tsallis and R\'{e}nyi entropies, which are monotone transformations of each other, are deformations of the celebrated Shannon entropy. Maximization of these deformed entropies, under suitable constraints, leads to the $q$-exponential family…
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional…
This paper introduces a novel approach to address inherent limitations in the Residual Power Series (RPS) method and its variants with Laplace-like transforms when applied to solving time-fractional differential equations. Existing methods,…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
In this paper we point out that the generalized statistics of Tsallis-Havrda-Charv\'at can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show…
We provide a necessary and sufficient condition for the representability of a function as the classical multidimensional Laplace transform, when the support of the representing measure is contained in some generalized semi-algebraic set.…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
We investigate the gravitational origin of the Tsallis entropy, characterized by the nonadditive index $\delta$. Utilizing Wald's formalism within the framework of $f(R)$ modified theories of gravity, we evaluate the entropy on the black…
A formalism proposed to study transverse Lambda polarization in unpolarized hadronic processes, based on a generalized pQCD factorization theorem, is extended to semi-inclusive DIS. Analytical expressions and examples of numerical estimates…
In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse…
In this paper, we begin by applying the Laplace transform to derive closed forms for several challenging integrals that seem nearly impossible to evaluate. By utilizing the solution to the Pythagorean equation $a^2 + b^2 = c^2$, these…
In this paper, a generalised integral called the Laplace integral is defined on unbounded intervals, and some of its properties, including necessary and sufficient condition for differentiating under the integral sign, are discussed. It is…
In this paper, a new method is developed to obtain explicit and integral expressions for the kernel of the $(\kappa, a)$-generalized Fourier transform for $\kappa =0$. In the case of dihedral groups, this method is also applied to the Dunkl…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
The use of average kernel method based on the Laplace transformation can significantly simplify the procedure for obtaining approximate analytical solution of Smoluchowski equation. However, this method also has its own shortcomings, one of…
In this paper, we derive a Laplace-type integral representations for both the generalized Bessel function and the Dunkl kernel associated with the rank-two root system of type B_2. The derivation of the first one elaborates on the integral…
The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a…