A remark on the Hankel determinant formula for solutions of the Toda equation

Abstract

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlevé II and IV equations are recovered. The case of finite lattice is also discussed.

arXiv comment14 pages, IOP style

References in corpus (1)

• Generating Function Associated with the Rational Solutions of the Painlevé II Equation

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