Jacobian elliptic function -- complex argument (u)

Discussion in 'Numerical Analysis' started by Gerald I. evenden, Oct 18, 2003.

  1. There is a sine series solution for sn(u|m) listed in
    Abramowitz & Stegun, p. 575, 16.23.1. Is the series
    legitimate if the argument u is complex?

    There is the mention of the special case of complex
    arguments on same page 16.21.1-->16.21.4. Is that the
    *only* way to compute the complex case of u?

    Many thanks.
     
    Gerald I. evenden, Oct 18, 2003
    #1
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  2. Gerald I. evenden

    Raymond Toy Guest

    Gerald> There is a sine series solution for sn(u|m) listed in
    Gerald> Abramowitz & Stegun, p. 575, 16.23.1. Is the series
    Gerald> legitimate if the argument u is complex?

    Don't know. But you can look at the expression for sn(x+i*y|m) to
    evaluate it in terms of functions of a real arg. This is in A&S
    somewhere (don't have it handy right now).

    Alternatively, you can use Landen's (or Gauss') transformation to
    compute it. Both are given in A&S. Maxima computes the elliptic
    functions this way.

    Ray
     
    Raymond Toy, Oct 20, 2003
    #2
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