Timeline for Does any research mathematics involve solving functional equations?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2011 at 20:17 | comment | added | Martin Rubey | Another nice example is the generating function for trees $A(x) = xE(A(x))$ where $E$ is the species of sets. | |
| Jan 27, 2011 at 15:55 | comment | added | Qiaochu Yuan | @Thierry: it is often more natural to write down a functional equation than a recurrence. For example, one definition of the Catalan numbers immediately gives C(x) = 1 + x C(x)^2, from which not only the standard recurrence but the standard closed form can be easily derived. There are more sophisticated examples (e.g. involving Lagrange inversion). | |
| Jan 27, 2011 at 15:25 | comment | added | Thierry Zell | Good point, though the question seems to be mostly about closed-form solution. I do have to ask: do you have a simple example of obtaining recurrences this way? I'm not a specialist, and the only examples I can think of off the top of my head go the other way around: finding a functional equation from known recurrences. | |
| Jan 27, 2011 at 14:23 | history | answered | ndkrempel | CC BY-SA 2.5 |