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I found a reference to the following article ;

O B Sheynin, The appearance of Dirac's delta functions in the works of P S Laplace (Russian), Istor.-Mat. Issled. Vyp. 20 (1975), 303-308, 381.

I don't have access to this nor can I read in Russian. Can anyone summarize this paper? I'm fairly familiar with the Laplace and other integral transforms, so a brief statement of and explanation of any nonstandard notation in the central formula or formulas as presented by Laplace would probably suffice.

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    $\begingroup$ I would glad to summarize but I do not have the paper. $\endgroup$ – Alexandre Eremenko Apr 2 at 2:47
  • $\begingroup$ @Alexander Eremenko, If I locate it, I'll send you a link. Thanks for the offer. $\endgroup$ – Tom Copeland Apr 2 at 3:03
  • $\begingroup$ DJVU copy of the volume can be downloaded from Историко-математические исследования. $\endgroup$ – Conifold Apr 2 at 13:00
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    $\begingroup$ According to the author, Laplace in a 1893 memoir "in fact introduces Dirac's delta-function, or more precisely, one of its interpretations, - the sequence of funtions (1) for $a\to\infty$". The sequence (1) is $\frac1{2a}\ln\frac{a}{|x|}$ from one of his early attempts to find the error curve. Of course, if this counts as "in fact introducing" the delta function then Fourier, Poisson, Fejer, Gauss, etc., "in fact introduced" it too. $\endgroup$ – Conifold Apr 2 at 13:23
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    $\begingroup$ @Conifold, perhaps you want to re-do your comment to correct '1893' to '1793'? $\endgroup$ – paul garrett Apr 2 at 15:46

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