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Results tagged with ca.classical-analysis-and-odes
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user 4672
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
5
votes
Infinite product experimental mathematics question.
Aha, I get Gjerji's insight, and I should have seen it sooner, but I was stuck on dealing with series representations by logarithms.
The second product looks like this:
$\sqrt[1]{\frac{2}{1}}\sqrt[ …
- 965
7
votes
2
answers
684
views
Infinite product experimental mathematics question.
A while ago I threw the following at a numerical evaluator (in the present case I'm using wolfram alpha)
$\prod_{v=2}^{\infty} \sqrt[v(v-1)]{v} \approx 3.5174872559023696493997936\ldots$
Recently, f …
- 965
2
votes
1
answer
334
views
Is there an nontrivial function whose 'period paralellograms' are Gosper Islands?
The Gosper island tiles the plane, so I'm curious if a nontrivial elliptic? function exists which would have a 'period gosper-island' instead of a period parallelogram. In this case, I'm using 'trivia …
- 965
11
votes
1
answer
467
views
turn $\pi/n$, move $1/n$ forward
start at the origin, first step number is 1.
turn $\pi/n$
move $1/n$ units forward
Angles are cumulative, so this procedure is equivalent (finitely)
to
$$
u(k):=\sum_{n=1}^{k} \frac{\exp(\pi i …
- 965