4
$\begingroup$

The image below describes an integration technique known (at least in Spanish) as "El Método Alemán," which translates to "The German Method" in English. I haven't found any references to this technique under the name "German Method" in English. This site cites the book Demidovich, B. P., and Aparicio, E. (2001). 5000 problemas de análisis matemático. Madrid, Spain: Thomson.

enter image description here

This video (in Spanish) gives an example of the application of the technique.

Does anyone know exactly what the origin of this method is? That is, who is the author and where was it published?

$\endgroup$
8
  • 1
    $\begingroup$ Possibly Demidovich himself? See this text. I suspect the "German method" more generally refers to undetermined coefficients, considering the frequent use of the German word ansatz in that context, but I don't have the sources to back up the claim that an unnamed German mathematician conceived of or is otherwise credited for it. $\endgroup$
    – user170231
    Commented Apr 1 at 17:29
  • 2
    $\begingroup$ In this answer, it is Hermite who is credited for this formula, which isn't surprizing, in connection with his work on elliptic functions. But maybe, it would be interesting to see if this formula isn't in the works of Jacobi ? $\endgroup$
    – Jean Marie
    Commented Apr 1 at 20:06
  • 2
    $\begingroup$ @B.A.M: In Spanish-speaking countries, the Ostrogradsky method is also known as the "Hermite-Ostrogradsky method." This seems to be consistent with what Jean Marie commented. But they are not exactly the same methods. $\endgroup$
    – Emmanuel José García
    Commented Apr 2 at 18:08
  • 1
    $\begingroup$ I've semi-crossposted your question to the History of Science and Math SE. Hopefully we can get to the bottom of the German-ness of this method. $\endgroup$
    – user170231
    Commented Apr 3 at 18:28
  • 1
    $\begingroup$ Probably better than the last link I shared: G.H. Hardy in The Integration of Functions of a Single Variable (1966) cites Hermite, with a footnote (p.52) pointing to the latter's Cours d'analyse (1875?). The method is described here (or appears to be, to my non-French eyes) $\endgroup$
    – user170231
    Commented Apr 4 at 14:49

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .