Favard constant

Summary

The Favard constants $K_0, K_1, K_2, \dots$ are explicit numbers given by alternating series of odd powers. They are the sharp constants in Jackson's inequality for periodic functions whose $r$-th derivative is bounded by $1$. They begin with $K_0 = 1$, $K_1 = \pi/2$ and $K_2 = \pi^2/8$, and they tend to $4/\pi$.