On the analytic form of the fundamental functions of one class of correlation integral equations

Abstract

Let’s consider a correlation integral equation of the form (see article). All conditions and remarks concerning this equation are fully preserved. To equations of this kind, as it is known, the problem of transforming a curvilinear correlation relation between two continuously distributed random variables into a rectilinear correlation relation between the new variables is reduced. It turns out that the problem of finding the set of all pairs of functions (in the case of symmetric correlation) between which the correlation is straightforward is equivalent to finding the fundamental functions of the equation.