We analyse the solution to the Thomas-Fermi equation discovered by Majorana. We show that the series for the slope at origin enables one to obtain results of accuracy far beyond those provided by available methods. We also estimate the radius of convergence of this series and conjecture that the singularity closest to origin is a square-root branch point.

中文翻译：

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关于Thomas-Fermi方程的​​Majorana解

我们分析了Majorana发现的Thomas-Fermi方程的​​解。我们表明，原点斜率的级数使人们可以获得的精度结果远远超出了可用方法提供的精度。我们还估计了该级数的收敛半径，并推测最接近原点的奇异点是平方根分支点。