On Functions of Second Kind in Orthogonal Polynomials Theory

An integral named after famous mathematicians Cauchy, Stieltjes, Hilbert, Schwartz, Riesz, Herglotz remains the center of attention of mathematicians specializing in different areas. This integral is a foundation of Analytic Functions Theory, Integral Transformations, Special Theory of Operators, Boundary Problems. This integral encompasses vast amounts of information. This integral also serves as a source, methodics amd one of the approaches to studying of orthogonal with respect to the weights p(x) on an interval [a,b] polynomials. The integral (see file for formula) was starting point for Chebyshev, Posse, Stieltjes, Heine and others when determining the relationship of Orthogonal Polynomials with continued fractions ([1}, [6]), which is considered the beginning of the Theory of Orthogonal Polynomials.