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Results tagged with legendre-polynomials
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user 35520
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Maximum of the Vandermonde determinant / minimum of the logarithmic energy
Write $V(a)$ for the determinant $\prod_{0\leq i<j\leq n-1} |a_i-a_j|$. Selberg's formula tells you that
$$\int_0^1 \cdots \int_0^1 V(a)^{2\beta} \prod_{i=0}^{n-1} da_i=
n! \prod_{j=0}^{n-1} \frac{(\ …
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