Combining three non linear functions into one single function

[souviktor]

combining three non linear functions into one single function...

I am performing one experiment in which I have a system output as Q which fundamentally depends on 3 independent inputs h,P,F.
i.e. Q=G(h,P,F)...where G is some function.
To quantify the dependence I varied h keeping P,F constant and got a variation in Q.

Similarly I got another experimental plot of Q vs P where h,F are constant
and also one Q vs F plot for constant h,P
I did a curve fit in MATLAB cftool and obtained some non linear functions.
The equations are of the following form
Q=a1*ln(h)+b1...P,F constant
Q=a2*P^b2+c2...h,F are constant...^ denotes exponentiation.
Q=a3*F^b3+c3...h,P are constant , ^ denotes exponentiation.
a1,a2,a3,b1,b2,b3,c2,c3 are all known constants.
what I want is to combine these three functions of h,P,F and obtain G such that Q=G(h,P,F)
any help?

 

[hotvette]

Taylor series approach might be fruitful. Since you have equations for the 1st partial derivatives of Q with respect to each of the three variables, you can calculate higher order partial derivatives.