Register to reply 
Termwise Differentiation of Power Series 
Share this thread: 
#1
Mar2908, 01:47 PM

Emeritus
Sci Advisor
PF Gold
P: 9,772

For those who don't know I'm writing a tutorial (Introduction / Summary of Differentiation) in the tutorials forum. I have come to the point of introducing Transcendental functions. I would like to introduce the exponential function first (via the Taylor series) and then present the natural logarithm as it's inverse. Although not entirely necessary, I would like to present a concise proof of termwise differentiation of power series in the tutorial.
If anyone knows of a concise online proof, or even better, would be willing to contribute a proof directly, please let me know, either in this thread or via PM. Thanks for your time. 


#2
Mar2908, 05:10 PM

P: 28

I would say that it follows from the linearity of differentiation



#3
Mar3008, 06:53 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682

Because you are talking about an infinite series, you also need the fact that a power series converges uniformly inside its radius of convergence.



Register to reply 
Related Discussions  
Nth Term Series  Calculus & Beyond Homework  7  
Divergent series and the limit of the nth term as n approaches infinity  Calculus  3  
Power series & Taylor series  Calculus & Beyond Homework  4  
Differentiation of a Power Series  Calculus  2  
Infinite series: nthterm test  Introductory Physics Homework  3 