Doob's martingale inequality: Difference between revisions

Latest revision as of 11:22, 3 October 2014

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-In [[mathematics]], the '''Favard constant''', also called the '''Akhiezer&ndash;Krein&ndash;Favard  constant''', of order ''r'' is defined as
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-:<math>K_r = \frac{4}{\pi} \sum\limits_{k=0}^{\infty} \left[ \frac{(-1)^k}{2k+1} \right]^{r+1}.</math>
-This constant is named after the French mathematician [[Jean Favard]], and after the  Soviet mathematicians [[Naum Akhiezer]] and [[Mark Krein]].
-==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 spline]]s.
-==References==
-* {{mathworld|urlname=FavardConstants|title=Favard Constants}}
-[[Category:Mathematical constants]]

Doob's martingale inequality: Difference between revisions

Latest revision as of 11:22, 3 October 2014

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