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This is a curious question about the way George Green could have defined his Green's function. All the definitions I see have only Dirac-delta $\delta(x-x')$ function as their source on the RHS. But the Dirac-delta was defined about a century after Green's work.

I just want to know, how George Green have defined his function (in case he defined it) ? In case he didn't define his Green's function, how did he give a hint about this method (without Dirac-delta function) ?

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    $\begingroup$ Suppose $L$ is a linear differential operator. The solution for $y$ to the differential equation $Ly=f$ if $f*g$ where $g$ is the Green's function and $*$ is convolution. It can be defined that way. But whether George Green did it that way I don't know. $\endgroup$ – Michael Hardy May 10 '14 at 17:19

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