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Complementary jacobi amplitude

  1. Apr 4, 2014 #1
    I found this identity in the wiki

    3381de258dc7b9d8733d05011c9811eb.png
    https://de.wikipedia.org/wiki/Jacob...efinition_als_spezielle_meromorphe_Funktionen

    One propertie of the ellipitc integral is: K(k') = K'(k), all this set of ideia seems answer an old doubt, ie, exist a complementary for jacobi amplitude?

    If

    ##\Delta(\phi, k) = \sqrt{1-k^2 \sin(\phi)}##

    thus

    ##\Delta(\phi, k') = \Delta ' (\phi, k) = \sqrt{1+k^2 \cos(\phi)}##

    ?
     
  2. jcsd
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