 Various methods have been developed that use approximate closed-form expressions to compute the nodes.As mentioned above, in some methods formulas are used as approximations to the nodes, after which some Newton-Raphson iterations are performed to refine the approximation.In a 2014 paper, Ignace Bogaert derives asymptotic formulas for the nodes that are exact up to machine precision for formula_13 and for the weights that are exact up to machine precision for formula_14 .