We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for $u(r,t)$ as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.

中文翻译：

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关于轴对称扩散方程的注释

我们考虑轴对称扩散方程的显式解。我们以梅林反演公式的形式重铸解决方案，并概述了一种计算公式的方法$u(r,t)$作为使用柯西剩余定理的系列。因此，我们能够将轴对称扩散方程的解表示为一个快速收敛的序列。