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

Complete minimal logarithmic energy asymptotics for points in a compact interval: a consequence of the discriminant of Jacobi polynomials