asymptotic equality
For the Lebesque constant of the classical Lagrange polynomial defined in the even number of nodes of interpolation, strict two-sided estimation is received. On this basis, an undefined value O(1) is refined in the well-known asymptotic equality for the Lebesque constant. Two actual problems in the interpolation theory associated with the optimal choice of O(1) are solved.
The paper deals with extremal properties of diagonal quadratic Hermite – Pad’e approximants of type I for exponential system {eλjz}2j =0 with arbitrary real λ0, λ1, λ2. Proved theorems complement known results of P. Borwein, F. Wielonsky.
