Bob Pego
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 Mar 23 awarded Good Answer Feb 17 answered Bounding a function of norms on the unit cube Feb 6 awarded Good Answer Nov 30 revised Is there a sequence such that $a_n\to0$, $na_n\to\infty$ and $\left(na_{n+1}-\sum_{k=1}^n a_k\right)$ is convergent? added 18 characters in body Nov 30 answered Is there a sequence such that $a_n\to0$, $na_n\to\infty$ and $\left(na_{n+1}-\sum_{k=1}^n a_k\right)$ is convergent? Oct 30 awarded Yearling Sep 21 answered Integrable slowly varying function Aug 20 comment Prove the theorem on analytic geometry in the picture. In higher dimensions, the analog is the Steiner formula which provides a polynomial expansion for the volume of the $t$-fattening'' of any convex set $K$ by the unit ball $B$: $$Vol_n(K+tB) = \sum_{j=0}^n \binom{n}{j} W_j(K)t^j ,$$ where the coefficients $W_j(K)$ are characterized by Hadwiger's valuation theorem. Jul 31 comment Have I just discovered an easy way to square numbers? @Anoneemus I think your insight is fun, thanks for sharing it. Seems to me it often can be faster and easier to remember to add $x$ and its successor than to remember to add $2x+1$. May 26 awarded Necromancer Jan 8 awarded Good Answer Oct 30 awarded Yearling Jun 13 answered What was the book that opened your mind to the beauty of mathematics? Jun 6 comment $p_n(x)=p_{n-1}(x)+p_{n-1}^{\prime}(x)$, then all the roots of $p_k(x)$ are real @Edwin I believe $p_0(x)$ is just some arbitrary polynomial, and is taken here to be of degree $m$. May 28 comment counterexample for ill posedness of the laplace equation "Laplace's equation" would be most accurate. May 24 comment Differentiable Path of Operators and their Inverses I'd suggest to consult one of the classic texts on operator theory for the relevant theory: Dunford and Schwarz vol. 1, or Kato's Perturbation Theory for Linear Operators, say. I think I recall that the calculation that ${\mathcal P}$ is a projection involves reducing a double integral to a single one. Basically, the point is that the contour $\Gamma$ encircles all the spectrum of $A(t)$ except zero. May 23 answered Differentiable Path of Operators and their Inverses May 13 comment Proving Taylor's Theorem by integrating n times? Perhaps this answer to a related question will help. In short: Apply the mean value argument to the n-fold integral first to pull out $f^{(n)}(\xi)$, then evaluate the n-fold integral with constant integrand. Apr 23 awarded Enthusiast Apr 22 answered How prove this integral inequality $6\left(\int_{0}^{1}f(x)dx\right)^2\le 1+ 8\int_{0}^{1}f^3(x)dx$