About the Fundamental Characteristics of the Lagrange Interpolation Polynomials Family

For the Lagrange interpolation polynomials family, determined in the even number of nodes, it is obtained various explicit (unmodulus) forms of the Lebesque functions. They are divided into uncrossing classes, which are consecutively studied using the elements of differential calculus then. The interdependence is established between the functions, as so as between the Lebesque constants from these classes.