*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. :(
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
branchandroot
no subject
Date: 2012-02-23 08:21 am (UTC)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. :(