Multiplicative version of Maclaurin or Talyor series

Question

Is there a multiplicative version of Maclaurin or Talyor series?

May be in the format

$\ln y = b_0 + b_1 \ln x + b_2 (\ln x)^2 + \cdots $

I want to use that as an approximation in a regression model.

Thanks, Yuzuru

Answer 1

I only recall a representation theorem in complex analysis (https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem#The_Weierstrass_factorization_theorem) but without more details about the function, not much can be said.

Note, however, that there is a bunch of specific method for nonlinear regression, e.g. http://es.mathworks.com/discovery/nonlinear-regression.html