指标方程有特殊根时三阶线性方程的解

The Solutions of Third Order Linear Equations,with the Indicial Equation Possessing Special Roots

用幂级数解法或合成解法解有正则奇点的三阶线性方程,它的指标方程的根之差为整数(包括重根)时,不能求全部解.但已知一个或两个解后,用降阶法可求所缺的解.用合成解法求解有极点的三阶线性方程,当指标方程有二重根时,由非重根得一个解.然后利用降阶法求所缺的解;指标方程有三重根时作变量变换可以求解.笔者解决了这些问题,与文献[1]一起构成了三阶线性方程的完整解法.

Solutions of third order linear equations with regular singular point are not all found with power series method or composition with the difference of roots of indicial equations as integer. These solutions are found with the method of reduction of order. If the roots of indicia] equation of third order linear equations are multiple roots, the solutions of those linear equations with pole can only be found with the method of reduction of order or with variable transformation.