  In this note we compute the logarithmic energy of points in the unit interval
$[-1,1]$ chosen from different Gegenbauer Determinantal Point Processes. We
check that all the different families of Gegenbauer polynomials yield the same
asymptotic result to third order, we compute exactly the value for Chebyshev
polynomials and we give a closed expresion for the minimal possible logarithmic
energy. The comparison suggests that DPPs cannot match the value of the minimum
beyond the third asymptotic term.
