Polynomial approximation ($E_n(f)={\inf }_{\mathrm{deg}p\le n}\Vert f-p{\Vert }_{\infty }$)

Polynomial approximation represents a function by polynomials of bounded polynomial degree. On a compact real interval, the Weierstrass approximation theorem guarantees uniform approximation of every continuous function by such polynomials. The displayed best error quantifies the accuracy available at degree at most $n$.