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.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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