Pade approximation

Question

I am trying to model the Pade approximation of a Lorentzian graph from the taylor series. I am trying to model PA[2/2] from taylor series expansion of order N+M=4th order of derivatives taken at the point of evaluation(x=x1).For ex:The function f(x) is expanded in taylor series up to the 4th order and compared with the coefficient of a0,a1,a2.As trying to solved, I get the coefficient in terms of a0 ,a1,a2 have orders up to 4th derivatives.Can the f(x) terms in some other expressions be replaced with the PA ratio expressions and solved further? As of now I am continuing to evaluate but seems very very lengthy after i put all the values of coefficients. Hope I am going in the right direction.