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Мemorial conference dedicated to the memory of Ivan Matveevich Vinogradov
March 28, 2019 14:30–14:55, Moscow, Steklov Mathematical Institute, Conference hall
 


Orthorecursive expansion of unity

A. B. Kalmyninab

a Department of Mathematics, National Research University "Higher School of Economics", Moscow
b International laboratory for Mirror Symmetry and Automorphic Forms, National Research University "Higher School of Economics" (HSE), Moscow
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A. B. Kalmynin
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Abstract: Define the sequence $c_n$ by relations
$$ c_0=1, \quad \frac{c_0}{n+1} + \ldots + \frac{c_n}{2n+1} = 0 $$
for all $n>0$. Despite simple definition, this sequence has interesting properties and turns out to be connected with orthorecursive expansions in the space $L^{2}[0,1]$. In my talk, I will discuss these properties (some of them are proved and some are observed experimentally) and tell you how permutations of the set of $n$ elements help us to prove that $c_n\neq 0$.

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