Related papers: Classical Lagrange Functions for the SME
In this note we prove mean convergence of Lagrange interpolation at the zeros of para-orthogonal polynomials for measures in the unit circle which does not belong to Szeg\H{o}'s class in the unit circle. When the measure is in Szeg\H{o}'s…
Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the…
In the variational approach to quantum statistics, a smearing formula describes efficiently the consequences of quantum fluctuations upon an interaction potential. The result is an effective classical potential from which the partition…
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…
We point out a formal analogy between lattice kinetic propagators and Haldane-Wu fractional statistics. The analogy could be used to compute the partition function of fractional quantum systems by solving a corresponding lattice kinetic…
The simulations of the light scalar mesons on the lattice are presented at the introductory level. The methods for determining the scalar meson masses are described. The problems related to some of these methods are presented and their…
The connection formula for the Jackson integral of type $BC_n$ is obtained in the form of a Sears--Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific bilateral multiple…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function…
The (classical) Lagrange spectrum is a closed subset of the positive real numbers defined in terms of diophantine approximation. Its structure is quite involved. This article describes a polynomial time algorithm to approximate it in…
This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-M\"untz functions presented by the authors recently. These basis functions are, in fact, generalizations form of the newly generated Jacobi…
A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
The Lagrange-mesh method is a very accurate procedure to compute eigenvalues and eigenfunctions of a two-body quantum equation. The method requires only the evaluation of the potential at some mesh points in the configuration space. It is…
We explore a hybrid expansion of the disturbing function in planetary dynamics that combines elements of the classical Laplace and Legendre developments. This formulation retains the structure of the Laplace expansion, but expresses the…
The techniques of dispersion relations match very well with those of effective field theory. I describe the techniques for using dispersion relations effectively, and give some pedagogical examples to illustrate the range of applications.
We explore the possibility of using the method of classical integral transforms to solve a class of $q$-difference-differential equations. The Laplace and the Mellin transform of $q$-derivatives are derived. The results show that the Mellin…
We introduce a sparse estimation in the ordinary kriging for functional data. The functional kriging predicts a feature given as a function at a location where the data are not observed by a linear combination of data observed at other…
The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products…