Related papers: Triple-Spherical Bessel Function Integrals with Ex…
Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are…
A new formula is derived that generalises an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, $P_l^m(x)$, of degree $l$ and order…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…
The Humbert-Bessel are multi-index functions with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…
We write, for geometric index values, a probabilistic proof of the product formula for spherical Bessel functions. Our proof has the merit to carry over without any further effort to Bessel-type hypergeometric functions of one matrix…
We extend the technique of using the Trapezoidal Rule for efficient evaluation of the Special Functions of Mathematical Physics given by integral representations. This technique was recently used for Bessel functions, and here we treat…
An infinite integral over four spherical Bessel functions is analytically evaluated for the special case when the arguments k_3=k_1 and k_4=k_2
We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products.…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation…
When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make…
In this article we study the Dyson Bessel process, which describes the evolution of singular values of rectangular matrix Brownian motions, and prove a large deviation principle for its empirical particle density. We then use it to obtain…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrated by obtaining a closed-form expression for the value of an…
In the article [11] of L. Kunyansky a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the…
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are…
A few approaches are derived to calculate three-particle integrals which include spherical Bessel functions of the first and second kind, i.e., the $j_{\ell}(V r)$ and $n_{\ell}(V r)$ functions. Such integrals are important in applications…
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…