Favard constant
From Wikipedia, the free encyclopedia
In mathematics, the Favard constant of order r is defined as
![K_r = \frac{4}{\pi} \sum\limits_{k=0}^{\infty} \left[ \frac{(-1)^k}{2k+1} \right]^{r+1}](../../../math/2/b/e/2bef47453b28f068ef714afd10da88b9.png)
This constant is named after the French mathematician Jean Favard.
[edit] Uses
This constant is used in solutions of several extremal problems, for example
- Norm of Euler spline
- Landau-Kolmogorov inequality
- Approximation of smooth functions by trigonometric polynomials [1]
[edit] References
- Eric W. Weisstein, Favard Constants at MathWorld.
