Related papers: Three-particle integrals with the Bessel functions
Jet-like three-particle azimuthal correlations can discriminate various physical scenarios that have been proposed to explain the observed strong modification to two-particle azimuthal correlations. The three-particle correlation analysis…
The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms…
Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of…
It is shown how to calculate asymptotics of integrals over the positive semi-axis of two functions related to the Degenerate Third Painlev\'e Equation (dP3). As an example, the corresponding results for the meromorphic solution of the dP3…
We examine indefinite integral involving of arbitrary power $x$, multiplied by three spherical Bessel functions of the first kind $j_{h},j_{k}$, and $j_{l}$ with integer order $h,k,l \geq 0$ and an exponential. Then we add some conditions…
This paper presents the equality of finite index sums of Bessel func- tions containing arbitrary numbers of terms. These reduce to the familiar three term recursion formulas in simple cases.
The number of parts in the partitions (resp. distinct partitions) of $n$ with parts from a set were considered. Its generating functions were obtained. Consequently, we derive several recurrence identities for the following functions: the…
Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic…
The equations describing the motion of finite-size particles (inertial particles) contain in their full form the history force. This force is represented by an integral whose accurate numerical evaluation is rather difficult. Here, a…
A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…
The products of the two and three bipolar harmonics ${\cal Y}^{\ell_1 \ell_2}_{LM}({\bf r}_{31}, {\bf r}_{32})$ are represented as the finite sums of powers of the three relative coordinates $r_{32}, r_{31}$ and $r_{21}$. The complete…
A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of…
The role of three-nucleon forces in ab initio calculations of nuclear systems is investigated. The difference between genuine and induced many-nucleon forces is emphasized. Induced forces arise in the process of solving the nuclear…
The current article completes our investigation of the hard-particle interaction by determining their distribution functionals. Beginning with a short review of the perturbation expansion of the free-energy functional, we derive two…
We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…
Based on known definite integrals of Bessel functions of the first kind, we obtain exact solutions to unknown definite integrals using the method of integral transforms from Hankel's transform.
Using relativistic tensor-bispinorial equations proposed in hep-th/0412213 we solve the Kepler problem for a charged particle with arbitrary half-integer spin interacting with the Coulomb potential.
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
Identities between Whittaker and modified Bessel functions are derived for particular complex orders. Certain polynomials appear in such identities, which satisfy a fourth order differential equation (not of hypergeometric type), and they…
Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…