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Results tagged with ca.classical-analysis-and-odes
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user 6153
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
2
votes
Evaluation of the following series... $S = 1/(2\times3) + 1/(5\times6) + 1/(7\times8) + 1/(1...
Anyway, I think the point is that with a(k) a sequence of the type implicated here, namely blocks of +1 and -1 alternating, jumping and flipping over at k any square, the generating function of the a( …
- 12.6k
1
vote
Accepted
Maximizing a Definite Integral Subject to Constraints
I think this isn't too bad, and your guess in below point (d) is justified. I doubt it depends on the detailed formulae.
Suppose we concentrate on g - f, which is constrained to have integral 0? And …
- 12.6k
7
votes
Looking for an interesting problem/riddle involving triple integrals.
Coffee mug problem: the volume of the part of a cylinder cut off by a plane, representing the volume of the coffee you have left when you first see the bottom of the mug. (Plane is horizontal, cylinde …
- 12.6k
1
vote
An inequality for a continuous non-smooth function
The inequality is easy to see by noting that (a) you have a function bounded near the origin, and (b) when you divide by |z| it tends to 0 at infinity. So it can be proved by a case analysis into two …
- 12.6k
4
votes
What is the difference between hard and soft analysis?
Cantor sets, then. I would expand the ternary Cantor set by a factor of three, note that this makes two disjoint copies, and conclude the measure was zero that way. A "soft" argument indeed. That does …
8
votes
Generalized Gauss-Green theorem
I sympathise on the "machinery". The general Stokes theorem is known to work with quite a lot of singularity on the boundary. I only know about this from (trying to read about it in) volume 9 of Dieud …
- 12.6k
1
vote
Limit connected with a periodic function
This type of question can be answered (typically) by applying (first) summation by parts, and then estimating sums of fractional parts. The sums of fractional parts can be handled by the Fourier serie …
- 12.6k
3
votes
On \ell_3 norm in R^2
So this asks for the general line L in the plane whether the minimum of the three-norm occurs at the point v obtained by dropping a perpendicular from 0 to L. Not true. Geometrically the tangents to t …
- 12.6k
0
votes
A question about the Kakeya problem
Don't you need a set of positive measure to swing a cat, even through 0.00001 radians? Intuitively you need to include a small sector of a circle to rotate a line segment about any of its points as fi …
- 12.6k
2
votes
Reference for complex analysis jargon
Conformal radius of a domain and Transfinite diameter seem to have most of these terms; see also http://en.wikipedia.org/wiki/Conformal_radius .
- 12.6k
7
votes
How should an analytic number theorist look at Bessel functions?
From the point of view of analytic number theory, the point usually would be asymptotic behaviour. This is typically well understood, and is in the massive book of Watson. Apart from that, yes, numero …
- 12.6k