Topic
Summation equation
About: Summation equation is a research topic. Over the lifetime, 4041 publications have been published within this topic receiving 77010 citations. The topic is also known as: discrete integral equation.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article , a probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given, and this interpretation is used to obtain an approximate solution for a generalization of the integral equation.
Abstract: A probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given. Then, this interpretation is used to obtain an approximate solution of a generalization of the integral equation. The approximate solutions are compared with the corresponding Neumann series solutions in various particular cases. AMS Subject Classification: Primary 45B05; Secondary 62M10, 93E20.
TL;DR: In this paper , a new integral equation that describes the behavior of the momentum space wave function for the one-dimensional Coulomb potential is proposed, which is a homogeneous Fredholm integral equation of the second kind and a singular integral equation, because its kernel has a singularity at some point in momentum space.
Abstract: A new integral equation that describes the behavior of the momentum space wave function for the one-dimensional Coulomb potential is proposed. The obtained result turned out to be a homogeneous Fredholm integral equation of the second kind and a singular integral equation, because its kernel has a singularity at some point in the momentum space. A nontriviality of the method of solving this singular integral equation lies in the application of the integral representation for its integral kernel. The technique applied in this paper made it possible to show that the wave function in the momentum representation is simultaneously a solution of the homogeneous Fredholm integral equation of the second kind and of the linear Volterra integral equation of the second kind. Since a linear Volterra integral equation of the second kind was easily transformed into a second order linear inhomogeneous differential equation with constant coefficients, the eigenfunctions and eigenvalues in the one-dimensional Coulomb problem were found without any difficulties. Such a circumstance may indicate the validity of the new integral equation and the proposed method of its solving.
Posted Content•
TL;DR: In this article, some applications of the non-homogeneous second order integral equation of Fox are considered in the context of number theory, and new solutions to Fox's integral equation are discussed in relation to number theory.
Abstract: We consider some applications of the non-homogeneous second order integral equation of Fox. Some new solutions to Fox's integral equation are discussed in relation to number theory.
TL;DR: In this paper, an exact formulation for the flow in a turbine lattice is provided, where the solution of the integral equation by successive approximation gives the potential and flow speed in analytical form.
Abstract: Integral equations provide an, exact formulation for the flow in a turbine lattice; solution of the integral equation by successive approximation gives the potential and flow speed in analytical form. If (3.16) and (4.7) are met, the process also converges to the exact value. This algorithm is comparatively readily, implemented with a medium-power computer.
TL;DR: In this article, a Fredholm integral equation of the first kind arising in contact problems for elastic foundations with voids is considered, and the uniqueness and solvability of the main integral equation are studied.
Abstract: The paper is concerned with a Fredholm integral equation of the first kind arising in contact problems for elastic foundations with voids. In the structure of its kernel there are two principal parameters. The first one is of a relative thickness of the strip foundation. The second one is coupled with the porosity of the material. We study uniqueness and solvability of the main integral equation, and then give explicit analytical asymptotics for the leading asymptotic term of the strip compliance, in the two limiting cases of thick and thin strip. Finally, analytical results are compared with results obtained by direct numerical treatment.