Recent content by liyz06

I know that (1+x)^n could be expanded easily by binomial theorem, but what I need here is to expand (1+x)^-n into polynomial form, not the reciprocal of a polynomial

Homework Statement How should I expand 1/(1+x)^n around x=0? Homework Equations The Attempt at a Solution

I get it now, use polar coordinate then it's z=\rho e ^{i\theta} \Rightarrow e^{-z^2}=e^{-\rho^2e^{2i\theta}}, the magnitude is really dependent on Re(e^{2i\theta})=\cos 2\theta>0, and that's where the |arg(z)|<\pi/4 from

Homework Statement Reading Hinch's book, there is a statement as follows: ... z need to be kept in the sector where exp(-z^2) ->0 as z -> infinity. Thus it's applicable to the sector |arg z|<pi/4...Homework Equations Why is this true and what is the limiting behavior of exp(x) for x in...

Thanks, really stupid question

Homework Statement I'm reading Hinch's perturbation theory book, and there's a statement in the derivation: ...\int_z^{\infty}\dfrac{d e^{-t^2}}{t^9}<\dfrac{1}{z^9}\int_z^{\infty}d e^{-t^2}... Why is that true?Homework Equations The Attempt at a Solution Homework Statement Homework Equations...