@sand15 

Yo, thanks a lot for your effort!

@Carl Love 

Thanks, that's what I thought, since there is an expression for indefinite sums in maple. However, I still don't get how to sum over  instead of i? And how to differentiate that expression. Also, whats the difference between the notation in fcn1 and fcn2 in my original question?

@mmcdara 

It contains a fitting parameter (omega) which is determined from experimental vapour pressure data. Thus, it improves the eos ability to predict vapour liquid equilibrium properties. 

It does not matter for the question though, since no derivative wrt T or anything is taken.

@mmcdara I think your forgot braces when transforming

p(T,v) -> f(T,v,p)=0. It should read + a/v^2, not -a/v^2

But anyway, thanks again for you answer!

@mmcdara

Thanks for your lovely answer, it helps a lot!

However, I don't quite agree with your statement that you cannot write p=f(T,v). This says that p is a function of T and v, which is true for a system of fluids in equilibrium. Especially for a perfect or ideal gas, pV/(nRT)=1. Which confirms that relation in my opinion. 

Though, I'm not very experienced with maple notation, so, judging by the two first answers, I got that wrong.

Thank you very much, that works for me!