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Re: Q: D[EllipticK[k],k] ?

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  • Subject: [mg2010] Re: Q: D[EllipticK[k],k] ?
  • From: "Brian J. Albright" <albright at>
  • Date: Thu, 14 Sep 1995 23:27:57 -0400
  • Organization: UCLA Department of Physics and Astronomy

"David O. Gunter" <david_gunter at> wrote:
>I need to know if it's possible to obtain the derivative of the
>complete elliptic integral given by EllipticK[k], where k is some
>parameter.  I've tried
>   D[EllipticK[k], k]
>with the output result
>   EllipticK'[k]
>and when I try
>   N[%] /. x->0.5
>I get
>   EllipticK'[0.5].
>How can I obtain the numerical answer this derivative?
>Thanks in advance.
>-david gunter

You might try numerically approximating the derivative:

  In[1]:= NEllipticK'[x_] = (EllipticK[x + eps] - EllipticK[x - eps])/(2 eps) +
                          O[eps^3 EllipticK'''[x]] /. eps -> 0.00001;

  In[2]:= NEllipticK'[0.5]

                           -15          (3)
  Out[2]:= 0.847213 + O[1. 10    EllipticK  [0.5]]

If the error in the derivative approx. is small enough for your purposes,
you can get the approximate numerical value from:

  In[3]:= Normal[%]

  Out[3]:= 0.847213



Brian J. Albright
Department of Physics and Astronomy, UCLA
albright at

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