We describe a method for the numerical evaluation of the angular prolate spheroidal wave functions of the first kind of order zero. It is based on the observation that underlies the WKB method, namely that many second order differential equations admit solutions whose logarithms can be represented much more efficiently than the solutions themselves. However, rather than exploiting this fact to construct asymptotic expansions of the prolate spheroidal wave functions, our algorithm operates by numerically solving the Riccati equation satisfied by their logarithms. Its running time grows much more slowly with bandlimit and characteristic exponent than standard algorithms. We illustrate this and other properties of our algorithm with numerical experiments.

翻译：我们描述一种方法,用于对第一种顺序为零的角形半行星波函数进行数字评估。它基于WKB方法所依据的观察,即许多第二顺序差异方程式所接受的解决方案,其对数比解决方案本身能更高效地代表其对数。然而,我们不是利用这一事实来构建预星形波函数的无症状扩张,而是用数字方法解决Riccati方程式的对数。它的运行时间比标准算法慢得多,带宽和特性比标准算法要快得多。我们用数字实验来说明我们的算法的这个和其他特性。