Marzo Sánchez, JordiOliver Santacreu, Júlia2021-06-032021-06-032020-06-21https://hdl.handle.net/2445/177922Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Jordi Marzo Sánchez[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.39 p.application/pdfcatcc-by-nc-nd (c) Júlia Oliver Santacreu, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Funcions hipergeomètriquesTreballs de fi de grauPolinomis ortogonalsTeoria de l'aproximacióIntegració numèricaHypergeometric functionsBachelor's thesesOrthogonal polynomialsApproximation theoryNumerical integrationinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess