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October 29th, 2012, 02:12 PM   #1
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Series solution near regular singular point

So you have and at is a regular singular point.

Therefore you plug in the generalized power series into the differential equation.
You should get:



soo... the indicial equation is




Now, for my question: Why do I consider r=1, but not r=0?

The back of the book only has as a solution. Why is r=0 not a solution? Is there a general rule on when to and when not to consider an indicial equation root?

Also, what if I've gotten ? or (where k is non-zero)?

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