Finding Green's function for diffusion equation

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Homework Statement


Find the solution for:
({\partial{}_t}^2 -D \Delta^2)G(\vec{r},t;\vec{r}_o,t_o)=\delta(\vec{r}-\vec{r}_o)\delta(t-t_o)
In two dimensions.

Homework Equations

The Attempt at a Solution


Am I supposed to use bessel eqs? I'm kind of stuck in starting the problem :L
 
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I suggest using Fourier and/or Laplace transforms.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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