  We give an effective method to compute the entropy for polynomials orthogonal
on a segment of the real axis that uses as input data only the coefficients of
the recurrence relation satisfied by these polynomials. This algorithm is based
on a series expression for the mutual energy of two probability measures
naturally connected with the polynomials. The particular case of Gegenbauer
polynomials is analyzed in detail. These results are applied also to the
computation of the entropy of spherical harmonics, important for the study of
the entropic uncertainty relations as well as the spatial complexity of
physical systems in central potentials.
