How to get the expansion results of the plasma dispersion function?

[Ising]

Hi:
The plasma dispersion function is:Z(m) = 1/SQRT(Pi) * Integral(-
Infinity,+Infinity) exp(-t^2)/(t-m) dt
The expansion of Z(m) for small argument m< 1 is found by Taylor
expansion of the above Cauchy integral and integrating term by term:
Z(m)=i*(Pi)^(1/2)*exp(-m^2)-2m*(1-2*(m^2)/3+4*(m^4)/15-......)
=(Pi)^(1/2)Sum[0,Infinity] {(i^(n+1))*(m^n))/(Gamma[1+n/2])
The asymptotic expansion for m >> 1 is given by
Z(m)=-1/m *(1+1/(2m^2)+3/4m^4)+.......)+ sigma * i*(Pi)^(1/2)*exp(-
m^2)
when Im[m]>0 sigma=0,
Im[m]=0 sigma=1;
Im[m]<0 sigma=2;
So my question is how the expansion results is got? The above resoluts
are commly seen in a textbook on plasma waves. I have work out the
case when m>1, but I could deduce the case when m<1! This problem
really puzzle for a long time!
For more clear description please see:
http://farside.ph.utexas.edu/teaching/plasma/lectures/node82.html
In the above page, how the deduce Equation (940) ?
Thanks for your reply!