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We show that the well known identity for the Wronskian of squared solutionsof a Sturm-Liouville equation follows from the Fay identity. We also study someodd-order (($2^n -1$)-order, $ n = 2, 3, ...$) identities which are specificfor tau functions, related to the KdV hierarchy.Comment: Amstex, 13 page

On the Fay identity for Korteweg–de Vries tau functions and the identity for the Wronskian of squared solutions of Sturm–Liouville equation