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We propose a method to compute, for a given potential model, an arbitrarycoefficient of the effective-range function expanded as a power series inenergy. The method is based on a set of recurrence relations at low energy,that allows a compact and general description to any order in energy forneutral and charged cases. By using the Lagrange mesh technique to compute theR-matrix at zero energy, this proposal permits to compute, with a very goodprecision, the effective-range parameters. We use a potential model for somenuclear systems to illustrate the effectiveness of this method and to discussits numerical limitations.

Precise determination of the effective-range parameters up to an arbitrary order