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本文用拉格朗日级数简练地推导出了常用铁路缓和曲线的一些新的有用的公式。如缓和曲线外一点到缓和曲线的距离公式,以及该点关于缓和曲线的垂足点上的弧长公式等等。也重新推导出了一些原有的公式,并纠正了个别公式的错误。对于一般的幂级数展开和变换问题,用拉格朗日级数比用常见的幂级数乘法或微分法要简捷和方便得多。因此它是一个值得提倡的方法。
In this paper, we concisely deduce some new and useful formulas of common railway curve by Lagrangian series. Such as the easing curve from the point to the easing curve of the distance formula, and the point on the curve of the foot point on the curve of the arc length formula and so on. It also re-derived some of the original formulas and corrected the errors of individual formulas. For general power series expansion and transformation problems, it is simpler and more convenient to use Lagrangian series than common power series multiplication or differentiation. So it is a worthwhile method to promote.