Favard constant
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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/8/c/5/8c51989e24e27d5316cdffef054ecd4e.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]
