# name
Quadratures de Txebixov a l’interval i Teorema de Bernstein

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Jordi Marzo Sánchez

# metadata.dc.description.abstract[].value
[en] In this work we will prove a theorem that Bernstein proved in 1937. This theorem states
that there are no quadrature formulas with equal weights (of Chebyshev) in the interval 
$[-1,1]$
$$
\int_{-1}^{1} f(x) d x \approx \frac{2}{n} \sum_{k=1}^{n} f\left(x_{k}\right)
$$
that are true for polynomials $f$ of degree $\leq n$, with nodes $x_{k} \in[-1,1]$, if $n \geq 10$.
We will also see some results related to the distribution of these nodes when $n$ is large.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Júlia Oliver Santacreu, 2020

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Quadratures de Txebixov a l’interval i Teorema de Bernstein