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

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

```"David O. Gunter" <david_gunter at qmgate.anl.gov> 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?
>
>
>-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

Regards,

-Brian

--
Brian J. Albright
Department of Physics and Astronomy, UCLA
albright at physics.ucla.edu
http://bohm.physics.ucla.edu/~albright

```

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