Favard constant

In mathematics, the Favard constant (also called the Akhiezer–Krein–Favard constant) of order ${\displaystyle r}$ is defined as^[1] $${\displaystyle K_{r}={\frac {4}{\pi }}\sum \limits _{k=0}^{\infty }\left[{\frac {(-1)^{k}}{2k+1}}\right]^{r+1}.}$$ The particular values of Favard constant are ${\textstyle K_{0}=1}$, ${\textstyle K_{1}={\frac {\pi }{2}}}$, ${\textstyle K_{2}={\frac {\pi ^{2}}{8}}}$.^[1]

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