Marvin Ray Burns

 I've been using Maple since 1997 or so.

MaplePrimes Activity


These are Posts that have been published by Marvin Ray Burns

As many of you know now the MRB constant = sum((-1)^n*(n^(1/n)-1),n=1..infinity).

Here are some equations involving various forms of that summation.

The first one involves convergent series and is too obvious. The others involve divergent series.

The last two, however, are new!

 

Let c=MRB constant and a, c~, x, and y = any number.

 

sum((-1)^n*(c~*n^(1/n)-c~),n=1..infinity)= c*c~.

evalf(sum((-1)^n*(n^(1/n)-a),n=1..infinity)) gives c-1/2*(1-a).

evalf(sum((-1)^n*(x*n^(1/n)+y*n),n=1..infinity)) gives (c-1/2)*x-1/4*y.

And it appears that

evalf(sum((-1)^n*(x*n^(1/n)-a),n=1..infinity)) gives (c - 1/2)*x + 1/2*a.

I want to Play with math full-time.  I posted a help me do it page on my website at marvinrayburns.com under the link titled "Help!" Any ideas on how I can gel it to go viral and maybe get some support from it?

The MRB constant can be computed in Maple by evalf(sum((-1)^n*(n^(1/n)-1),n=1..infinity)).

On my laptop restart; st := time(); evalf(sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity), 500); time()-st gives a timming of 37.908 seconds.

Using the procedure posted at the bottom of this message st := time(); A037077(500); time()-st gives a much faster timing of 1.903 seconds.

My fastest timing for 500 digits of MRB comes from my...

A better approximation gives more digits of accuracy in the result per digit of precision used in the computation than a good approximation does.  I was wondering if anyone could come up with a better approximation to the MRB constant than 31/165, 

The MRB constant Z will probably have several parts.

The following example is from the Maple help pages
> with(GraphTheory);
> with(SpecialGraphs);
> H := HypercubeGraph(3);
DrawGraph(H)
 
 


What I would like to do in the MRB constant z,  MRB constant z part2, and etc. is to draw a series of graphs that show the some of the geometry of the MRB constant.

See http://math-blog.com/2010/11/21/the-geometry-of-the-mrb-constant/. I would like to draw a tesseract of 4 units^4, a penteract of 5 units^5, etc and take an edge from each and line the edges up as in Diagram 3:

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As usual I'm asking for your help.

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Download May262012.mw

 

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