Does this summation be finite: $$\sum_{l=1}^{\infty} \int_{[a,b]}\left(\frac{d^l}{dx^l} f(x)\right)^2 dx.$$ obliviously if $f(x)$ is a polynomial the property it's ok, but for regular continuos functions? Can we extend this for multivariate functions with partial derivates? It's a quasi-norm?
2026-03-26 18:58:43.1774551523
Summation of function's derivate
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The sum need not be finite. Consider $f(x)=e^x$. Then each term in your sum is the same positive constant.