Exercise 6, § 2

Functions of a Real Variable, VII, 328

Let $V_n$ be the Vandermonde determinant $V(1, 2, \ldots, n)$ (Alg., III, p. 532). Show that

\log V_n = \frac{n^2}{2} \log n - \frac{3n^2}{4} + \left( \frac{1}{2} \log 2\pi - \frac{1}{4} \right) n - \frac{1}{12} \log n + k + O \left( \frac{1}{n} \right)

where

k

is a constant.

Solution

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