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: David Billinghurst
Date: Thu, 20 Sep 2012 07:58:05 +1000
On 20/09/2012 2:13 AM, Raymond Toy wrote:
>
>
> On Tue, Sep 18, 2012 at 3:30 AM, David Billinghurst
> <dbmaxima at gmail.com <mailto: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
Yes. There should be a %pi/2. The taylor series of the hypergeometric
function representation works, so I have a way forward.
I know we worked around a similar problem with another special function
- forget which - by changing the form of the derivative, but I can't see
an obvious alternative.