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
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...
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...