Favard constant

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (April 2023) (Learn how and when to remove this message)

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

${\displaystyle K_{r}={\frac {4}{\pi }}\sum \limits _{k=0}^{\infty }\left[{\frac {(-1)^{k}}{2k+1}}\right]^{r+1}.}$

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

Particular values

${\displaystyle K_{0}=1.}$

${\displaystyle K_{1}={\frac {\pi }{2}}.}$

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.

References

• Weisstein, Eric W. "Favard Constants". MathWorld.

This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e