  The electrostatic interpretation of zeros of Jacobi polynomials, due to
Stieltjes and Schur, enables us to obtain the complete asymptotic expansion as
$n \to \infty$ of the minimal logarithmic potential energy of $n$ point charges
restricted to move in the interval $[-1,1]$ in the presence of an external
field generated by endpoint charges. By the same methods, we determine the
complete asymptotic expansion of the logarithmic energy $\sum_{j\neq k}
\log(1/| x_j - x_k |)$ of Fekete points, which, by definition, maximize the
product of all mutual distances $\prod_{j\neq k} | x_j - x_k |$ of $N$ points
in $[-1,1]$ as $N \to \infty$. The results for other compact intervals differ
only in the quadratic and linear term of the asymptotics. Explicit formulas and
their asymptotics follow from the discriminant, leading coefficient, and
special values at $\pm 1$ of Jacobi polynomials. For all these quantities we
derive complete Poincar\'e-type asymptotics.
