| Abstract: | 若方程式 f(x,y) = a0(x)+a1(x)*y+a2(x)*y2+...+an(x)*yn = 0, ai(x)∈C(x)∗, 我們要找出解 y(x) = x^{r1}(c1 + x^{r2}(c2 + x^{r3}(c3 + ...))), r2,r3,r4,...> 0, 並討論 y(x) 分支的情形以及何時會出現 {r1,r2,r3,...} 的最小公分母, 最後再算 y(x) 的收斂範圍。
If we have an equation that is f(x,y) = a0(x)+a1(x)*y+a2(x)*y2+...+an(x)*yn = 0, ai(x)∈C(x)∗, we want to find solutions which are of the form x^{r1}(c1 + x^{r2}(c2 + x^{r3}(c3 + ...))), r2,r3,r4,...> 0, and we will discuss the bifurcation of y(x) and when the lowest common denominator of {r1,r2,r3,...} appears. Finally, we compute the range of convergence of y(x) expansion. |
