Register to reply 
Summation helpby FrogPad
Tags: summation 
Share this thread: 
#1
Apr2207, 07:02 PM

P: 837

I don't see how the following works:
[tex] \sum_{n=0}^\infty \delta ( n  n_0 ) z^{n} = z^{n_0} [/tex] I am missing the steps from [itex] \sum_{n=0}^\infty \delta ( n  n_0 ) z^{n} [/itex] to [itex] z^{n_0} [/itex]. If I try this step by step: [tex] \sum_{n=0}^\infty \delta ( n  n_0 ) z^{n} = \sum_{n=0}^\infty \delta ( n  n_0 ) z^{n_0} = z^{n_0} \sum_{n=0}^\infty \delta ( n  n_0 ) [/tex] Now, how is [itex] \sum_{n=0}^\infty \delta ( n  n_0 ) [/itex] equal to 1. I don't get that. Thanks 


#2
Apr2207, 07:30 PM

Sci Advisor
HW Helper
Thanks
P: 25,228

delta(nn0) is equal to 1 if n=n0 and zero otherwise. So the only way the sum could be nonzero is if n0 is a positive integer. Is n0 a positive integer?



#3
Apr2207, 07:45 PM

P: 837

Thanks man :) Yeah, n0 is a positive integer. time for a break... 


Register to reply 
Related Discussions  
Summation x(1/2)^x  Calculus & Beyond Homework  2  
Help with summation  Calculus & Beyond Homework  10  
Summation of S(N)?  Linear & Abstract Algebra  7  
Can the summation.  Introductory Physics Homework  17  
Sum of (i^2)/(4^i) where i is from 0 to infinity.  Introductory Physics Homework  13 