Global maximum of ?(x)-x : local maximum between .42 and .5

[Gerald McGarvey]

I'm considering using the box function (started on it but not finished) and
programming the search for the maximum/minimum in a given interval,
using PARI. I don't know if using PARI will suffice or if Mathematica or
Maple is required to get sufficient precision. If PARI is up to the job, it
will take me some time to program the automation of the search, I'll have
to learn some more PARI programming. I might need some guidance
from a PARI wizard (if anyone would like to volunteer).

This web page (a rough, unfinished draft that might contain errors):
http://www.linas.org/math/chap-minkowski/chap-minkowski.html
made me start to realize how deep this function is (I only understand some 
of it).
This function is a real beauty.

It does seem to be of considerable interest and worthy of effort to pursue 
this.

- Gerald

At 10:56 PM 6/14/2006, Gene Smith wrote:


>On 6/13/06, Gerald McGarvey 
><<mailto:Gerald.McGarvey at comcast.net>Gerald.McGarvey at comcast.net> wrote:
>The local maximum of ?(x)-x between .42 and .5 appears to occur at an
>interesting
>value of x. I believe it occurs at around .460495713337621635801842 which
>has a
>continued fraction beginning as
>[0, 2, 5, 1, 4, 1, 4, 1, 4, 1, 4, 1, 5, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 5,
>1, 4, 1, 4, 1, 4, 1,
>
>
>I think it would be of considerable interest to push this farther.  Has 
>anyone considered using box rather than the ? function? I continue to 
>suspect it would be easier.
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20060614/f6f7cdd4/attachment-0001.htm>