# Talk:MRB constant

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## Why is this remarkable?

I'd be interested in any sort of proof that this infinite sum was not something evaluable in closed form. But since that kind of result is what one would generally expect, I'm somewhat at a loss to understand what is remarkable about this constant. Am I missing the point? Charles Matthews (talk) 21:34, 8 May 2009 (UTC)

The series $\sum_{k=1}^{\infty} (-1)^k k^{1/k}$ diverges. Remarkable is that its partial sums are bounded. And the MBR constant is simply the upper limit for them. Maxal (talk) 00:39, 28 August 2009 (UTC)

## Irrationality

• If irrationality is not proved, it has to be stated as such. It is at least misleading to call a number irrational if its irrationality is not proved. Maxal (talk) 11:30, 26 January 2011 (UTC)
• Per WP:AB, in clear-cut case, I corrected the statement concerning irrationality.Marvin Ray Burns (talk) 20:10, 1 February 2011 (UTC)

## Continued fraction representation

In case anyone cares to put it in the article, here is a continued fraction representation of the MRB constant Wolfram Alpha (26 January 2011). "Wolfram Alpha". Wolfram research. Retrieved 26 January 2011. [0; 5, 3, 10, 1, 1, 4, 1, 1, 1, 1, 9, 1, 1, 12, 2, 17, 2, 2, 1, 1, 17, 1, 6, 4, 1, 3, 3, 4, 2, 1, 262, 2, 1, 4, 1, 49, 2, 1, 9, 1, 2, 1, 1, 4, 23, 26, 6, 6, 5, 3, 3, 1, 1, ...] The source is http://www.wolframalpha.com/input/?i=MRB+constant&t=elg01. Marvin Ray Burns (talk) 21:24, 17 October 2010 (UTC)

## The Geometry of the MRB constant

For consideration in the article:

At http://math-blog.com/2010/11/21/the-geometry-of-the-mrb-constant/ there is a brief introduction to the geometry of the MRB constant.Marvin Ray Burns (talk) 03:42, 6 February 2011 (UTC)

## Classical Analysis and the MRB constant

For consideration in the article:

There is a Cornell University paper done on the MRB constant and its integral analog that can be found at http://arxiv.org/abs/0912.3844.Marvin Ray Burns (talk) 04:11, 6 February 2011 (UTC)