A generalized form of Laguerre equation is obtained by using a transform, which can be applied directly to the eigenvalue problem of an equation satisfied by the radial function of a hydrogen-like ion, and further transformation to get the asymptotic solution of the radial equation is avoided. 利用变换得到了连带拉盖尔方程的推广形式,可以直接用在类氢离子的径向波函数所满足的方程的本征值问题上,无需利用渐近解的形式对径向方程作进一步的变换。