Taylor series of elliptic_kc(m) about m=0 fails with error
Subject: Taylor series of elliptic_kc(m) about m=0 fails with error
From: Raymond Toy
Date: Wed, 19 Sep 2012 09:13:10 -0700
On Tue, Sep 18, 2012 at 3:30 AM, David Billinghurst <dbmaxima at gmail.com>wrote:
> Taylor series of elliptic_kc(m) about m=0 fails with
> maxima-5.28.0/gcl/windows and clisp/windows.
>
> taylor(elliptic_kc(m),m,0,1);
>
> Maxima encountered a Lisp error:
> Error in MACSYMA-TOP-LEVEL [or a callee]: Bind stack overflow.
> Automatically continuing.
> To enable the Lisp debugger set *debugger-hook* to nil.
>
Sorry about that. This is a known problem. I don't know how to teach
taylor about expansion. Powerseries also fails for elliptic_kc
Elliptic_ec has the same problem.
>
> According to A&S 17.3.11
>
> K(m) ~= 1 + (1/2)^2 m + (1.3/2.4)^2 m^2 + ....
>
I think you're missing a %pi/2 factor there. :-)
Ray