Expressing as a single sum.

  • Thread starter David Laz
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  • #1
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I know this is pretty easy, but for this particular question I'm having difficulty.
its for the Power series solution of the DE y''+yx=0

[tex]
\sum\limits_{n = 0}^\infty {(n - 1)nC_n } x^{n - 2} + \sum\limits_0^\infty {C_n } x^{n + 1} [/tex]

This is ths sum I've come up with and I need to express it as a single sum. I can't seem to do it though. Any help will be greatly appreciated.
 

Answers and Replies

  • #2
665
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David Laz said:
I know this is pretty easy, but for this particular question I'm having difficulty.
its for the Power series solution of the DE y''+yx=0
[tex]
\sum\limits_{n = 0}^\infty {(n - 1)nC_n } x^{n - 2} + \sum\limits_0^\infty {C_n } x^{n + 1} [/tex]
This is ths sum I've come up with and I need to express it as a single sum. I can't seem to do it though. Any help will be greatly appreciated.
Well, what do you know about the sum of series with the same indices?
 
  • #3
86
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The index of your first sum is not correct.

Remember that every time you take a derivative you loose a constant term.

After you correct your index you can then change it to something more desirable.
 
  • #4
Tide
Science Advisor
Homework Helper
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Incidentally, if you didn't know, your DE is just a variant Airy's Equation (with x replaced by -x) and represents waves propagating in a medium whose properties (index of refraction, water depth, etc.) vary linearly in space.
 
  • #5
28
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Excellent. Thanks for the help.

I believe we study Airy's equations in greater detail later on in the course. We touched on them briefly in my Quantum Physics class last semester though. :D
 

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