Calculation Nv(x) of complex order v numerically, we must calculate Df{JN+ε(x)}. When Df{JN+ε(x)} is calculated by the recurrence method, this letter will analyze the error of Df{JN+ε(x)}, and will determine the optimum number of recurrences.

We frequently need to calculate the Neumann function Nν(x) of complex order ν numerically in order to solve boundary problems on electromagnetic fields. This paper presents a new method for the numerical calculation of Nν(x) of complex order ν. This method can calculate Nν(x) precisely even when the order ν is close to an integer n, and the algorithm by the method is very simple.