Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

We continue our investigation on the newly introduced concept of the τ function [1], associated with monodromy preserving deformations of a linear differential equation $\text{dY}\text{dx}\text{= A(x)Y}$. In this paper a series of τ functions parametrized by integers are introduced. Their ratios to the original τ function are then shown to be explicit rational expressions in terms of the coefficients of A(x). We point out, and follow where possible, a close analogy between the theory of τ functions and that of classical theta functions.