I obtained a series expansions as this type
$$f(x)=g(x)^{\textstyle \sum_{i=0}^{n}\alpha_{i}x^{i}+O\left(\tfrac{1}{x^{n+1}}\right)}$$
what is the exact name of this formula
I obtained a series expansions as this type $$f(x)=g(x)^{\textstyle \sum_{i=0}^{n}\alpha_{i}x^{i}+O\left(\tfrac{1}{x^{n+1}}\right)}$$ what is the exact name of this formula 


It's a pretty ordinary asymptotic expansion for $$\frac{\log f(x)}{\log g(x)}.$$ 

