How to derive Zamolodchikov's recursion relation of conformal block?

Question

Could any one explain how to derive the recursion relation, equation (7) of Zamolodchikov's paper http://link.springer.com/article/10.1007%2FBF01214585? 

I understand that there is when \(F(D,di,C,x)\) will diverge when c becomes closer to \(c_{mn}\), so there should be a pole. But how do we know that it's the form of\(\frac{1}{c−c_{mn}}\)instead of \(\frac{1}{(c−c_{mn})^2}\) or other forms?