Thanks for your kind replies
I need an asymptotic series in general which contains S0, because S0 in my actuall analysis is the postion of a phase change problem. which changes after time to time. Thats why I need a general form. I have numerical results for it, but I am interested in asymptotic.
My main equation which conatin the discuss part (which we now are playing with to get asymptotic series) is
For the above equation i need asymptotic series.