# Green functions

1. Jun 8, 2006

### JohanL

I need a list of Green functions,
for different types of equations and dimensions.

I have tried to use google but with no success.

2. Jun 8, 2006

### rcgldr

I got a bunch of hits with a google for "green's theorem", but I'm not sure if there are other functions you're looking for.

3. Jun 8, 2006

### FredGarvin

Green functions are not the same thing as Green's Theorem.

I can't honestly say that I have seen anything tabulated. I can't say that I have ever looked for anything like that though either. I was always under the impression that green fuctions are dependent on boundary conditions and the Diff. Eq's being used. I'll keep my eyes open to see if I find anything. You might try searching with "Green's functions" as well. I have heard them refered to in both ways.

EDIT: The first hit I got using the "green's function" search...
http://mathworld.wolfram.com/GreensFunction.html

4. Jun 8, 2006

### JohanL

Thx. Yes they are dependent on boundary conditions. But for the more simple cases i was sure to find tables of green functions.

Something like

$$-\frac {1} {2\pi}ln(\rho_1- \rho_2) ;\frac {i} {4}H_0[k(\rho_1- \rho_2)];\frac {1} {2\pi}K_0[k(\rho_1- \rho_2)]$$

for Laplace, Helmholtz and modified Helmholtz in the plane when G goes to 0 as r goes to infinity.
And also in 3 dimensions, for a sphere with homegenous diricihlet on the boundary, the diffusion equation, the wave equation etc.

Green functions are very useful when solving P.D.E and therefor i thought i could find some good tables. But none of my mathematical handbooks have this and i havent found any on internet yet either.

Last edited: Jun 8, 2006
5. Jun 8, 2006

### pmb_phy

There exists no such list since a "Green Function" is any function whose Laplacian equals $\delta$(|x-x'|). There is an infinity of such functions.

Pete

6. Jun 8, 2006

### jarvis

Green functions are not confined to differential equations containing the Laplacian, they work under an arbitrary differential operator. The Green function is by definition the solution to a differential equation under application of a unit impulse source term. The beautiful thing about Green functions is that once I know the solution for a unit impulse, I can obtain the solution for an arbitrary source by a convolution of the Green function with that source. This is of course predicated on linearity of the solutions.

7. Jun 8, 2006

### WMGoBuffs

Check out the first chapter or two of Jackson Electrodynamics for everything you would ever care to know about green functions.

8. Jun 10, 2006

### JohanL

Thats the Green function for the Laplace operator.
How is a general green function different from general solutions to ODEs, integrals etc? There are tables of those.
I found a short table of green functions in Arfken.

9. Jun 10, 2006

### JohanL

Thx, but thats probably Laplace and Poisson differential operator only?

10. Jun 10, 2006