Chirp

[davv]

*chirps*

I just thought I should meep or chirp to say I'm not completely dead. Just busy with differential equations and partial fractions and isoclines and all that stuff - since I'm going to take a test as part of moving (if however slowly) towards my shiny papers.

Yes, I should have known this about... ten years ago. But that time has already passed.

Also, I suppose there have been other things going on, it's just that when I'm doing various other things, I don't find the time to report on here, and so when I do go back and say "hey, it's awfully empty in here", there has been so much time since the things actually happened that I can't really sum them up :)

So... meep! Are there any other meeping critters around? Or perhaps some chirping ones, or even shiny crows?

Meep :)

Comments

[lhexa]

I do remember, though I'm puzzled by you saying you're doing that analytically now. Having a power series is the very definition of analyticity.

I'm going through one of my periods of self-doubt, but at least I continue to learn interesting new things during those periods. Just today, though, my advisor warned me about the risk of never doing research because of thinking you need to learn more in order to do it...

[davv]

Yeah, I noticed that after I posted. I was thinking of closed form.

If I had gone a little step further and observed that the power sums were actually combinations of the power sums for exponential expressions, then I could have written the functions as those. But I didn't, and you know what they say about hindsight!

Just today, though, my advisor warned me about the risk of never doing research because of thinking you need to learn more in order to do it...

I've never encountered that particular problem. One does research to find something new (or at least new to oneself), after all. But if you learn new things during those periods, at least there's that.

[lhexa]

*grins* If you're still having fun with series, try sticking complex numbers into some of them and see the stuff you get. There are some neat and surprising identities! Also, any convergent Taylor series for real numbers will also be an analytic complex function, conveniently.

Complex numbers are actually much more well-behaved than real ones, in this matter... if a complex function is differentiable, then it's differentiable to all orders, and has a series expansion to boot. Those things don't always go together for real functions. *shuts up now*

The problem in question is thinking "I'm stuck on this research problem involving brackets, so I'll go read more about Lie groups or differential geometry or topology until it all makes sense" where it might already be the case that I know everything I need to know to solve the problem. :(