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