Expansion of the Solutions of a Gauss-Manin System at a Point of Infinity

convergent near the point $(t_{0}, t)=(\infty, 0)$ at infinity, where $-\Lambda$ is the matrix of exponents of $f$ shifted by N. In the present article, we shall determine such an expansion of $\Phi$ in an explicit manner for typical examples of Gauss-Manin systems. Our computational results will be given in \S 3. The polynomial $f(x)$ to be deformed is assumed there to belong to either of the types