A new and generic algorithmic approach for calculating the derivatives of order n of the Erlang-B function with respect to the number of servers, involving a recursive matrix relation, is presented. A detailed analysis of the propagation conditions of the relative error of the successive terms given by the recursion when the initial values are calculated with certain error, is performed. Among various results it is proved that this error always decreases (in a certain sense) and tends asymptotically to a constant value which can be very small. Computational results, comparing the efficiency and accuracy of the method with an alternative algorithm using cardinal series quadrature, show a good performance for the proposed method in a wide range of the arguments of the function.
