一种Kummer类型的微分方程及其严格解

A Kummer's Type Differential Equation and Its Exact Solution

以级数展开的方法 ,严格求解了一个二阶变系数微分方程 ,讨论了解函数的对称性及其收敛性。通过与已知的其他特殊函数的比较发现 ,运用适当的自变量的代换 ,方程的解可用已知的合流超几何函数来表示。并且在此代换下 。

A type of second order differential equation is exactly solved by using the series expansion method.The symmetry and diversity of the solution function are discussed.It is found that the solutions may be expressed by the confluent hypergeometric function,and that,after transforming the variables,the original equation can be transformed to a Kiummer equation.