About: Summation equation is a(n) research topic. Over the lifetime, 4041 publication(s) have been published within this topic receiving 77010 citation(s). The topic is also known as: discrete integral equation.
01 Mar 1968-American Mathematical Monthly
01 Jan 1962-Journal of the ACM
TL;DR: Here the authors will consider only nonsingular linear integral equations of the first kind, where the known functions h(x), K(x, y) and g(x) are assumed to be bounded and usually to be continuous.
Abstract: where the known functions h(x) , K(x, y) and g(x) are assumed to be bounded and usually to be continuous. If h(x) ~0 the equation is of first kind; if h(x) ~ 0 for a -<_ x ~ b, the equation is of second kind; if h(x) vanishes somewhere but not identically, the equation is of third kind. If the range of integration is infinite or if the kernel K(x, y) is not bounded, the equation is singular. Here we will consider only nonsingular linear integral equations of the first kind:
01 Jan 1992-
15 Apr 1963-Physical Review Letters
Abstract: ABS>The equation of state and the pair distribution for the Percus- Yevick integral equation for the radiai distribution function of a classical fluid are obtained in closed form for the prototype of interacting hard spheres. (D.C.W.)
01 Jan 1984-
Abstract: As shown in Sects 31, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (31, 31) For nonlinear Langevin equations (367, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker  and Planck : many review articles and books on the Fokker-Planck equation now exist [15 – 15]