Expanding a small oscillation potential in taylor series

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I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.
 
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see http://en.wikipedia.org/wiki/Taylor_series" [Broken]
 
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I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.
Not many people have this book. Maybe you should take a screen shot and upload it? From what you're saying, I don't see why you would need a Taylor series for the energy of an oscillating mass. It is already quadratic with the displacement (for a spring-mass system at least).
 

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