How to develop in series?

  • #1
How to develop in series as in the image below? What does the third term signify?
1462258388878.jpg
 

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  • #2
Orodruin
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It is a simple Taylor expansion of the relativistic energy.
 
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  • #4
What does the third term signify?
1462261373421.jpg
 
  • #5
Ibix
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It doesn't have a name or any particular meaning as far as I am aware.

If you are measuring the energy of particles, say, when v is high enough for this term to be measurable then you ought to be using the relativistic formula for energy. Below that velocity the Newtonian approximation is good enough.
 
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