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In what work did Jacobi introduce the jacobian, and what was his motivation for doing so?

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I don't know about the motivation, but it was introduced in his article Ueber die Functionaldeterminanten (Journal für die reine und angewandte mathematik, bd. 22, 1841). However, Jacobians had already been studied by Cauchy in 1815.

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    $\begingroup$ The motivation is described at length in the article of Stackel, in the same file that you linked. It follows Jacobi's article. $\endgroup$ Dec 11, 2017 at 0:16
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    $\begingroup$ @AlexandreEremenko Thank you. I failed to notice it. $\endgroup$ Dec 11, 2017 at 7:17
  • $\begingroup$ Was Jacobi aware of Cauchy's use of jacobians? $\endgroup$
    – user109871
    Dec 11, 2017 at 13:13
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    $\begingroup$ @user109871 He doesn't seem to mention Cauchy in his article. $\endgroup$ Dec 11, 2017 at 13:18

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