[Maxima-bugs] [ maxima-Bugs-1165488 ] elliptic_kc and diff

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Bugs item #1165488, was opened at 2005-03-17 13:52
Message generated for change (Comment added) made by rtoy
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1165488&group_id=4933

Category: Lisp Core
Group: None
>Status: Closed
>Resolution: Fixed
Priority: 5
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: elliptic_kc and diff

Initial Comment:
The dérivative of elliptic_kc gives 2 times the exact
value.

To remedy 

1. make a lisp file that contains

(defprop %elliptic_kc
    ((m)
     ;; diff wrt m
     ((mtimes) ((rat) 1 2)
      ((mplus) ((%elliptic_ec) m)
       ((mtimes) -1
	((%elliptic_kc) m)
	((mplus) 1 ((mtimes) -1 m))))
      ((mexpt) ((mplus) 1 ((mtimes) -1 m)) -1)
      ((mexpt) m -1)))
  grad)

(the same function as in .../maxima/5.9.1/src/ellipt.lisp 
modified by the "((rat) 1 2)" )

2. load this file at the beginnig of a session.

That's all.

To see the error 

plot2d([(elliptic_kc(x+0.001)-elliptic_kc(x))/0.001,diff(elliptic_kc(x),x)],[x,0.1,0.9]);

the two curves are : a discrete derivative of
elliptic_kc and the exact derivative. 



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>Comment By: Raymond Toy (rtoy)
Date: 2005-03-18 12:37

Message:
Logged In: YES 
user_id=28849

Fixed.  Thanks.

This can also be seen by differentiating elliptic_f(phi,m)
wrt m and substituting %pi/2 for phi.

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