Favard constant - Alchetron, The Free Social Encyclopedia

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

K r = 4 π ∑ k = 0 ∞ [ ( − 1 ) k 2 k + 1 ] r + 1 .

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

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.

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