
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 15th, 2011, 10:58 AM  #1 
Senior Member Joined: Aug 2008 Posts: 133 Thanks: 0  a question about a power series
If we let be deltation, its commutative and associative, we find addition is distributive across it: , and that it is defined by the following recursion formula: , multiplication across deltation also behaves as exponentiation across addition. So the question I had was, what's its taylor series? I managed to work out the first five derivatives, I'm gonna leave out the steps, I just wonder if someone can maybe help me out with the algorithm or if they've seen these coefficients somewhere before (or maybe someone knows a technique for iterated differentiation): Interestingly enough, the coefficients always add up to one. The obvious choice is to center the taylor series about y, so if therefore the taylor series will look something like this: where etc... So thanks for reading if you got this far, any help would be greatly appreciated. 

Tags 
power, question, series 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
In need of help disk, series test, taylor, and power series  g0bearmon  Real Analysis  2  May 22nd, 2012 01:10 PM 
Power series index shift question  Splint  Complex Analysis  0  February 13th, 2012 06:50 PM 
3rd power series question  thegle  Calculus  4  February 26th, 2010 08:59 PM 
another power series question  thegle  Calculus  2  February 26th, 2010 06:01 PM 
Power Series Question  WannaBe  Real Analysis  2  January 19th, 2010 11:10 AM 