Re: [Maxima-discuss] significant difference?

[Raymond T. <toy...@gm...>]

>>>>> "Peter" == Peter van Summeren <pet...@gm...> writes:

    Peter> Hello,

    Peter> I am checking a book from Miroslav Lutovac for the nomen q(k)=e^(-pi * K'/K) of the elliptic functions.

    Peter> He gives for k=sin(86degrees) a q of 0.2954883855586914 on page 512.

    Peter> I did:


    Peter> q(k):= (%e)^(-%pi * elliptic_kc(1-k^2)/elliptic_kc(k^2));

    Peter> q(sin(%pi * 86/180)),numer;

    Peter> And got: 0.2954883855586907

    Peter> It is a very small difference - only in the last two digits, but is it significant for something wrong?

    Peter> Can anyone check this result?

Some notes.  sin(%pi*88/180) produces 3 rounding errors for the arg,
then then some error for sin.  This is k.  You then compute 1-k^2,
This loses some accuracy since k is close to 1.  It's probably more
accurate to comput 1-k^2 = (1-k)*(1+k).

elliptic_kc has some error, and computation of the ratio does too.
Another round-off for multiplying by pi and finally, some error for
the computation of the exponential.

So, the result is pretty good.  Could it be better, and still use
double-float numbers?  Probably.  Having functions of k instead of m
would help.  An algorithm for q(k) would probably also help instead of
using the definition of q(k).

--
Ray