Re: [Maxima-discuss] significant difference?

[Peter v. S. <pet...@gm...>]

Hello,
Thanks to all for help.
Wish list:
1. the nome q(k) as optimized procedure (the Jacobi nome is basic for the
calculation of elliptic functions)
2. the same for K(k)/K'(k) ( used for designing elliptic filters).
There are many more useful functions for designing elliptic filters.
With friendly greetings,
Peter

Op ma 10 jun. 2019 19:41 schreef Raymond Toy <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
>
>
>
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