ABSTRACT An integrating factor is presented involving the terms in and of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey second-order differential equations, rather than being given by quadrature. The new factors provides old and new integrals for special functions which obey such differential equations. The functions considered here are cylinder functions, parabolic cylinder functions and Whittaker functions. All the integrals given have been checked using Mathematica.

中文翻译：

---

特殊函数不定积分的第三个积分因子

摘要 提出了一个积分因子，它涉及一般齐次二阶线性常微分方程中的项和项。新的积分因子服从二阶微分方程，而不是由正交给出。新因子为服从此类微分方程的特殊函数提供了新旧积分。这里考虑的函数是圆柱函数、抛物线圆柱函数和惠特克函数。所有给定的积分都已使用 Mathematica 进行了检查。