A Generalization of a Minimal Problem of Korkin-Zolotarev kind

This is an English translation of the paper in which N. I. Akhiezer discovered his famous orthogonal polynomials on two intervals in a connection with a generalization of the Korkin-Zolotarev (Korkine-Zolotaref) problem (see the small commentary by P. Yuditskii, at-tached to the current publication). Translated from German by F. Puchhammer. §1. If one intends to approximate a continuous function f(x) defined on the interval [−1, 1] by polynomials, one has to define the distance between two continuous functions on [−1, 1] first, and then try to obtain the coefficients of the polynomial Pn(x), such that the distance between f(x) and Pn(x) becomes as small as possible. Usually, either the quantity max −1≤x≤1 |f(x) − Pn(x)| or the quantity ∫ 1