Why Do Certain Mathematical Functions Use Asymptotic Expansion Series?

[kari_convention]

Hello and good day. I am searching for Asymptotic Series for my Mathematical Technique mini project. I'm doing Asymptotic Expansion Series and the examples of it. I search on the internet and I found few examples of it such as Gamma Function, Error Function, Riemann Zeta Function, Exponential Integral and Multiple Integral.
But my lecturer have giving me some twist, he asked me to find why all the examples that I found, choose Asymptotic Expansion Series instead of other expension series.

Thanks.

 

[kari_convention]

anyone?

thanks.