Favard constant explained

In mathematics, the Favard constant, also called the Akhiezer - Krein - Favard constant, of order r is defined as

K _{r} = (4)/(\pi) \sum\limits ^{inf ty} _{k =0} \left[ (( -1 ) ^{k})/(2 k +1) \right] ^{r+1} .

This constant is named after the French mathematician Jean Favard, and after the Soviet mathematicians Naum Akhiezer and Mark Krein.

Particular values

K _{0} = 1 . K _{1} = (\pi)/(2) .

Uses

This constant is used in solutions of several extremal problems, for example

• Favard's constant is the sharp constant in Jackson's inequality for trigonometric polynomials
• the sharp constants in the Landau–Kolmogorov inequality are expressed via Favard's constants
• Norms of periodic perfect splines.