1)thanks, and 2)automatic proves of identities with elliptic functions?
Subject: 1)thanks, and 2)automatic proves of identities with elliptic functions?
From: David Billinghurst
Date: Mon, 04 Nov 2013 19:53:32 +1100
On 3/11/2013 6:52 PM, Igor Korepanov wrote:
> Now one more question. My current aim is actually to (guess correctly - this is done already - and then) prove a certain identity between Jacobi elliptic functions. That my identity does hold, there is no doubt - because numeric calculations with any precision (and randomly chosen parameters) show this. And I know from a book entitled "A=B" by Petkov?ek, Wilf and Zeilberger that identities with elliptic functions are proved, in our enlightened age, automatically - but using, alas, Maple or Mathematica. So, my obvious question is - what about Maxima?
Igor,
There are some functions for simplifying equations containing Bessel
functions and exponential integrals in
share/contrib/diffequations/contrib_ode.mac,
see
http://sourceforge.net/p/maxima/code/ci/master/tree/share/contrib/diffequations/contrib_ode.mac.
Recurrence relations are applied systematically to reduce the order of
the functions, and if all goes well the expression simplifies to 0.
A similar approach may work with Jacobi elliptic functions. Can you
provide an example.