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Results tagged with ca.classical-analysis-and-odes
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user 527142
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Prove that $\lim\limits_{n\to\infty}\left(\sum\limits_{r=0}^{n-1}\sqrt{1-\frac{r^2}{n^2}}-\f...
I came across the above question in a mathematical problem. It is not difficult to see that
$$
\lim\limits_{n\to\infty}\left(\frac{1}{n}\sum\limits_{r=0}^{n-1}\sqrt{1-\frac{r^2}{n^2}}\right)=\int\limi …
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