相关论文: A versatile integral in physics and astronomy
This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
A review of the path integral approach to quantum cosmology and its relation to canonical quantisation. The initial derivation of the Hartle-Hawking and Vilenkin wavefunctions from the Euclidean Einstein-Hilbert action, and later, from the…
We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic…
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…
We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.
Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra of…
Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
If the prime numbers are pseudo-randomly distributed, then analogy with quantum systems suggests that counting primes might be modeled by a non-homogeneous Poisson process. Consequently, postulating underlying gamma statistics, more-or-less…
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
We prove a pair of transformation formulas for multivariate elliptic hypergeometric sum/integrals associated to the $A_n$ and $BC_n$ root systems, generalising the formulas previously obtained by Rains. The sum/integrals are expressed in…
We explore some integrals associated with the Riesz function and establish relations to other functions from number theory that have appeared in the literature. We also comment on properties of these functions.
The physics of nuclear reactions in stellar plasma is reviewed with special emphasis on the importance of the velocity distribution of ions. Then the properties (density and temperature) of the weak-coupled solar plasma are analysed,…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
This paper focuses on a wide class of Collatz-type arithmetic dynamics, and presents a systematic derivation of recursive formulas and functional equations satisfied by the associated generating functions. The main tools belong to complex…
We study properties of the general integral transform defined for a family of hypersurfaces in a smooth manifold. Estimates of Sobolev norms, range conditions and approximation theorem for the kernel of the integral transform are stated.…
Numerical methods for fractional calculus attract increasing interests due to its wide applications in various fields such as physics, mechanics, etc. In this paper, we focus on constructing high-order algorithms for Riesz derivatives,…