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If you have a system with equally distributed temperature, and in the center of it is inserted a point source of heat (a point hotter than the rest of the system) after a given amount of time this heat is dispersed through the system in a way that the points closer to the center are hotter than the ones farther from it.

What is the function of the distance that describes more precisely the temperature distribution in this system?

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Here is the complete derivation for this solution. If you have any questions about the derivation feel free to post here and I'll try to help.

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I was thinking of implementing this solution in my application, but I don't know how to implement it in the computer language I'm currently using (python)... – Jader Dias Feb 16 at 15:57
I'm not sure I follow. Python has all the standard mathematical functions. Worse case you can brute force your way through your domain calculating the solution for each x,t combination. Something to check might be to see if python handles vector math which would make the coding a little easier. What exactly are you having trouble with? – Kathe♦ Feb 16 at 21:12
@Kathe Integration en.wikipedia.org/wiki/Integral – Jader Dias Feb 17 at 14:28
@Kathe There is also a the sum from one to positive infinite – Jader Dias Feb 17 at 14:31
So if I recall my PDE's class correctly you will generally get the infinite sum dropping out when you solve for your specific initial and boundary conditions or the series will converge to some other function. Otherwise you are correct, there is no way to take an explicit infinite sum on a computer, what you would have to do is prove that the series converges and then set a tolerance where you would discard the last bit of the series. – Kathe♦ Feb 18 at 22:16

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