Numerical evaluation of the Erlang function through a continued-fraction algorithm

There exist in the literature various approaches for the evaluation of the Erlang function for both integer and non-integer values of the parameter. These approaches have permitted the computation of tables. However, different methods may be more appropriate to the treatment of special problems, for example, the optimization of telephone networks. Previously known methods make no use of a continuous algorithm. This latter method would make it possible to reach the required accuracy by selecting the appropriate number of terms from a convergent series, a continued fraction, or even an asymptotic expansion. The continuous algorithm also makes treatment of the problem easier by a computer.