We construct two rational approximate solutions to the Thomas–Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the predicted numerical values of the two approximate solutions, we compare these values with an accurate numerical solution obtained using a fourth-order Runge–Kutta method. We also present several new integral relations satisfied by the bounded solutions of the TF equation.

中文翻译：

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基于动态一致性的Thomas–Fermi方程的​​近似有理解

我们构造了Thomas-Fermi（TF）非线性微分方程的两个有理近似解。这些表述源自动态一致性原理的应用。除了检查两个近似解的预测数值的差异外，我们还将这些值与使用四阶Runge-Kutta方法获得的精确数值解进行比较。我们还提出了TF方程的有界解满足的几个新的积分关系。