求解变系数线性常微分方程的一种新的解析算子法
A novel analytical operator method to solve linear ordinary differential equations with variable coefficients
摘要：
本文讨论了一种新的解析算子法，它可用于求解具有正则奇性的线性常微分方程。解以解析级数形式和梅林-巴恩斯型围道积分形式给出。利用递推关系得到了级数的精确解，不需要计算级数系数，对于非齐次方程，不需要显式计算格林函数，齐次方程和非齐次方程的解是一致的，对于数学物理中出现的所有特殊函数，都得到了封闭解.对于一个二阶方程的两个独立的解决方案，而不调用朗斯基，即使当指数相差一个整数。
英文摘要：
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series solution is obtained without having to calculate series coefficients by recurrence relation.Both homogeneous and inhomogeneous equations are solved identically without having to calculate the Green's function explicitly in the case of inhomogeneous equation.Closed-form solutions are obtained for all the special functions appearing in mathematical physics. For a second-order equation both the independent solutions are obtained without invoking Wronskians, even when the indices differ by an integer.
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