To regress g^{E} or g^{E}/RT^{ }precisely, mostly the Redlich-Kister expansion or a Legendre-polynomial is used. The advantage of the Legendre polynomial lies in the simple calculation of the derivatives required for the calculation of the activity coefficients. As the Redlich-Kister expansion, the Legendre polynomial is used to expand the parameter A of the Porter expression g^{E}=A*x_{1}*x_{2}^{ }as function of composition:

g^{E} = x (1-x) ( a_{1} Q_{1} + a_{2} Q_{2} + a_{3} Q_{3} + ..... )

with a_{1}, a_{2}, a_{3}, ..... adjustable parameters

and Q_{1} = 1

Q_{2} = 2x-1

Q_{k} = ((2k-3)(2x-1)Q_{k-1} - (k-2)Q_{k-2})/(k-1)