Talk:Harmonic function
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Dumb question: what's "harmonic" about a harmonic function ? It was one of the reasons I came to the page, but I didn't get an answer. unlikely_ending 11:19, 5 November 2006 (UTC)
- I understand that at least one reason why harmonic functions are so-called is that if you look for solutions of Laplace's equation (i 3-dim, say) which are products F(x)G(y)H(z) of functions of each variable separately, then you end up with 3 differential equations for x, y, z, whose solution is essentially 'Simple Harmonic Motion'. Madmath789 11:54, 5 November 2006 (UTC)
Can somebody write down how harmonic functions are connected to stochastic processes? or else leave this point away in the description.
- This is a tough one, as the connections between harmonic functions and stochastic processes is quite deep - you have to know a lot about both potential theory and measure-theoretic probability theory to understand it, unfortunately. I don't think it would be easy to explain the connction in this article without making ot way too technical (I certainly would not attempt to do it!) You can get an idea of the problem by looking at Doob's book 'Classical Potential Theory and Its Probabilistic Counterpart'. Sorry if this does not really answer your query! Madmath789 11:54, 5 November 2006 (UTC)
[edit] Vote for new external link
Here's my site full of PDE's with harmonic functions. Someone please put it in the external links if you think it's helpful!
http://www.exampleproblems.com/wiki/index.php/PDE:Laplaces_Equation
