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I have some historical questions in connections for the notes to a book I am writing.

Who the first person to discover that the Coulomb potential in two dimension is $\log(|x|^{-1})$, equivalently that this is essentially the fundamental solution for the 2D Poisson equation? I'm guessing it might have been Poisson in one of his remarkable papers between 1817 and 1818. These papers are not readily available to me.

Also who first used the term logarithmic potential?

I'm also interested in the discrete case. My understanding is that the discrete fundamental solution was first discussed in Polya's famous 1921 paper on recurrence in random walks. Can anyone confirm that and if that is also the place where the $\log(n)$ asymptotics was found (so far as I can see from skimming his paper with my almost non-existent German, all he used is that it goes to infinity).

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  • $\begingroup$ Re "Poisson in one of his remarkable papers between 1817 and 1818" Could you cite these publications, please? They may be available as scans online, but I am having trouble identifying relevant publications by Poisson in the stated timeframe. Could you likewise cite "Polya's famous 1921 paper"? $\endgroup$
    – njuffa
    Dec 21, 2023 at 7:39
  • $\begingroup$ Here is a scan of one of his papers from 1817: Poisson, "Sur la forme des intégrales des équations aux différences partielles." Bulletin des sciences / par la Société philomathique de Paris, 1817, pp. 180-183 $\endgroup$
    – njuffa
    Dec 21, 2023 at 8:03
  • $\begingroup$ Poisson, "Remarques sur les rapports qui existent entre la propagation des ondes à la surface de l'eau, et leur propagation dans une plaque élastique." Bulletin des sciences / par la Société philomathique de Paris, 1818, pp. 97-99 $\endgroup$
    – njuffa
    Dec 21, 2023 at 8:11
  • $\begingroup$ Poisson, "Sur l'intégrale de l'équation relative aux vibrations des plaques élastiques." Bulletin des sciences / par la Société philomathique de Paris, 1818, pp. 125-128 $\endgroup$
    – njuffa
    Dec 21, 2023 at 8:16
  • $\begingroup$ Poisson, "Mémoire sur le mouvement des fluides élastiques dans les tuyaux cylindriques, et sur la théorie des instruments à vent." Bulletin des sciences / par la Société philomathique de Paris, 1818, pp. 43-45 $\endgroup$
    – njuffa
    Dec 21, 2023 at 16:37

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