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Results tagged with ca.classical-analysis-and-odes
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user 126667
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
11
votes
Accepted
Truncated product of $\zeta(1)$?
Formula (8) on this page gives the result
$$\prod_{p \le n} \frac1{1-p^{-1}} = e^\gamma \log n \,(1 + o(1)).$$
- 26.3k
8
votes
Uncountable preimage of every point
No. For example, let $g : [0, 1] \to [0, 1] \times [0, 1]$ be a continuous surjective map (space-filling curve) and let $p : [0, 1] \times [0, 1] \to [0, 1]$ be the projection onto the first coordina …
- 25.2k
5
votes
level sets of multivariate polynomials
I don't know how to estimate the measure of the level sets, but I can answer the question about the number of connected components to an extent. Let $P_f(x) = (x-1)(x-2)\cdots(x-f)$, and define $p(x_ …
- 25.2k
4
votes
Is there a topological description of combinatorial Euler characteristic?
Why isn't there an intrinsic topological description, or perhaps manifold-theoretic description?
At least in some cases, the combinatorial Euler characteristic of X is equal to the homotopy Euler …
- 25.2k