In fact i have some questions:

Let us suppose we have the series:

f(g)=a0+a1g+a2g**2+.. where g is the coupling constant and a0,a1,a2,a3..an are numerical values (real or complex)

then just suppose that some of them a1,a5,a7 for example give an infinite value...how could you re-arrange the series or what trick is used to remove these infinites

If all the an where infinite ..how could you remove them?..