Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with ca.classical-analysis-and-odes
Search options not deleted
user 2757
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
29
votes
Are there any nonlinear solutions to $f(x+1) - f(x) = f'(x)$?
Yes, there exist nonlinear solutions.
Multiplying by $e^{x+1}$ and setting $g(x):=e^x f(x)$ transforms the question into finding a solution to $g(x+1)=eg'(x)$ not of the form $e^x(ax+b)$.
Start with …
- 23.8k
21
votes
Accepted
A two-variable Fourier series and a strange integral
Here is a proof of the conjecture, a proof that also shows how to compute the integrals explicitly.
The proof is somewhat similar to David Speyer's approach, but instead of using multivariable residu …
- 23.8k
8
votes
Asymptotic series for roots of polynomials
This is the well-known theory of Puiseux series (substitute $T=1/n$ to match the notation in that website). The convergence of the series is mentioned there too. So in your dissertation, I would rec …
- 23.8k
4
votes
Accepted
Can I detect the point of impact without looking at it?
Andrew's comments showed me that in my first answer I was misunderstanding several aspects of his question. Since I am still not entirely sure that I am capturing the spirit of the problem, let be be …
- 23.8k
3
votes
Can I detect the point of impact without looking at it?
The answer is that everything can be recovered, if $f$ is chosen suitably!
There are $2^{\aleph_0}$ possibilities for $c$, so we can fix an injection $c \mapsto u_c$ from the set of possible $c$ into …
- 23.8k