球对称时空中格林函数的Pade逼近
Pade Approximants of the Green Function in Spherically Symmetric Spacetimes
摘要：
我们研究了球对称时空中的标量格林函数，它表示为点的分离中的坐标级数展开式。计算了标量格林函数的Hadamard参数中函数$V(x,x')$的高阶级数展开式。这种扩展，然后使用调查的系列的收敛性，并估计其收敛半径。使用Pade逼近的方法，我们表明，该系列可以扩展超出其收敛半径的正常邻域边界的短距离内。
英文摘要：
We investigate the scalar Green function for spherically symmetric spacetimes expressed as a coordinate series expansion in the separation of the points. We calculate the series expansion of the function $V(x,x')$ appearing in the Hadamard parametrix of the scalar Green function to very high order. This expansion is then used to investigate the convergence properties of the series and to estimate its radius of convergence. Using the method of Pade approximants, we show that the series can be extended beyond its radius of convergence to within a short distance of the normal neighborhood boundary.
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