Related papers: Three-particle integrals with the Bessel functions
We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm,…
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
The set of particle-hole ring diagrams for a many-fermion system in two dimensions is studied. The complex-valued polarization function is derived in detail and shown to be expressible in terms of square-root functions. For a…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…
Contour integrals of rational functions over ${\cal M}_{0,n}$, the moduli space of $n$-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined…
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson…
In this paper, we obtain a general expression for the entries of the r. (r is integer) power of a certain n-square complex tridiagonal matrix. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell…
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
We report on a considerable improvement in the technique of measuring multiparticle correlations via integrals over correlation functions. A modification of measures used in the characterization of chaotic dynamical sytems permits fast and…
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
The interaction of particles in an electrolytic medium can be calculated by solving the Poisson equation inside the solutes and the linearized Poisson--Boltzmann equation in the solvent, with suitable boundary conditions at the interfaces.…
The approach of direct integration of the three-dimensional Faddeev equations with respect to the breakup T-matrix in momentum space for three bodies of different masses is presented. The Faddeev equations are written out explicitly without…
We present a list of formulae useful for Weyl-Heisenberg integral quantizations, with arbitrary weight, of functions or distributions on the plane. Most of these formulae are known, others are original. The list encompasses particular cases…
In a recent paper we unified Bessel functions of different orders .Here we extend the unification to other linairely independant solutions to Bessel equation, Neumann's and Hankel's functions
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
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…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
In this article we exploit the fact that the special relativistic formula which relates the energy and the 3-momentum of an elementary particle with its rest mass, resembles the pythagorean theorem for right triangles. Using such triangles,…
Fix $\lambda>0$. Consider the Bessel operator $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ on $\mathbb{R_+}$, where $\mathbb{R_+}:=(0,\infty)$ and $dm_\lambda:=x^{2\lambda}dx$ with $dx$ the Lebesgue measure. We…