I think that Ge(s) = tiny / s^2 + O(1/s), s --> 0. The tiny / s^2 term might be due to rounding of the floats in Ge.
(%i16) e : taylor(rationalize(Ge(s)),s,0,2)$
(%i17) lopow(e,s);
(%o17) -2
(%i24) bfloat(rectform(coeff(e,s,-2))), fpprec : 200;
(%o24) 9.8480154028659045663685635665[145 digits]04666166039093880989658562b-20*%i+2.2564140069591173798376206889[145 digits]79608157633058364356016944b-20
Trying various values of fpprec makes me think that %o24 is nonzero.
--bw
________________________________________
From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu] on behalf of Robert Dodier [robert.dodier at gmail.com]
Sent: Monday, May 07, 2012 23:41
To: maxima at math.utexas.edu
Subject: Re: [Maxima] plotting modulus of complex function
On 2012-05-07, Bart Vandewoestyne <Bart.Vandewoestyne at telenet.be> wrote:
> On 05/04/2012 05:25 PM, Robert Dodier wrote:
>> foo(s):=abs(Ge(s))$
>> for n thru 16 do print(bfloat(foo(1.0b0/10^n)))$
> Hmmm... interesting... so according to Robert, the limit for s->0 is
>
> 2.3b-4 (a constant)
>
> while Raymond Toy's conclusion in another reply appears to be approximately
>
> (4.5e-23+%i*3.8e-24)/s (1/s behavior)
>
> Note the dramatic difference between these two! Which of these two is
> closest to the real truth (close to 0, the Ge(s) behaves as a constant
> OR as a 1/s singularity) is *exactly* what I'm interested in :-)
Bart, if you try the loop I suggested but work closer to 0 (by
increasing n to, say, 50) I think you will see it blow up. The value is
approximately constant for a while (maybe up to n = 20 or so) but then
it starts growing. Whether it's approximately 1/s or not, I didn't
investigate carefully.
Hope this helps,
Robert Dodier
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