I am looking at the relativistic relationship between energy and momentum and I want to use a Taylor expansion to estimate the Energy at very large and very small values for momentum (p).
The equation is $E^2 = p^2c^2+m_0^2c^4$
I know that for small values of p, E is roughly equal to $\frac{p^2}{2m_0}+m_0c^2$, but I do not know how to use the Taylor Expansion to do find what E is roughly equal to at very large values of p. Thank you for any help.
Maybe something like this? $$ E = pc \sqrt{1 + \frac{m_0 c^2}{p^2}} \simeq pc (1 + \frac{m_0 c^2}{2p^2} ) $$