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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( …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar
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 .
Charles Matthews's user avatar
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 …
Charles Matthews's user avatar