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