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Power series recurrence relations

  • #1
190
0

Homework Statement


In the following series':

http://image.cramster.com/answer-board/image/cramster-equation-2009410014306337491927047975008434.gif

According to my book, we only have a common range of summation here for n >= 2.

Therefore we need to treat n = 0 and n = 1 separately.

We thus write:

[2r(r-1) + 3r - 1]c0 = 0

and

[2(r+1)r + 3(r+1)-1]c1 = 0

My question is in both cases we ignored the last (4th) series to develop these two equations. How can we just ignore this power series?

I imagine it must be because its summation begins at n=2 unlike the others, but why are we allowed to ignore it up until n = 2?

Thanks!


Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 
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Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi IniquiTrance! :smile:

(try using the X2 and X2 tags just above the Reply box :wink:)
According to my book, we only have a common range of summation here for n >= 2.

Therefore we need to treat n = 0 and n = 1 separately.

We thus write:

[2r(r-1) + 3r - 1]c0 = 0

and

[2(r+1)r + 3(r+1)-1]c1 = 0

My question is in both cases we ignored the last (4th) series to develop these two equations. How can we just ignore this power series?

I imagine it must be because its summation begins at n=2 unlike the others, but why are we allowed to ignore it up until n = 2?
ah, but you're really writing:

([2r(r-1) + 3r - 1]c0 + 0)xr = 0

and

([2(r+1)r + 3(r+1) -1]c1 + 0)xr+1 = 0,

so you're not really ignoring the 4th sum at all, you're just not bothering to put in the zeros. :wink:

Alternatively, think of the 4th sum as starting at n = 0 like the others, and with c-1 and c-2 defined as 0 :smile:
 
  • #3
190
0
Ah, ok much clearer now. Thank you!
 

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