About the MRB Constant








				it follows that

For what value of x is f(x)=x^(1/x) a maximum?

f'(x)=x^(1/x-2)(1-lnx)=0,

x=e and gives a maximum of e^(1/e)=1.444667861...

user90369
(https://math.stackexchange.com/users/332823/user90369),
High precision evaluation of the series $\sum_{n=3}^\infty
(-1)^n (1-n^{1/n})$, URL (version: 2019-07-16):
https://math.stackexchange.com/q/3294599

where A is the Glaisher-Kinkelin constant.

here

formulas (11)+(16)+(19).

CMRB from Steiner's Problem


CMRB

Dark Malthorp
(https://math.stackexchange.com/users/532432/dark-malthorp),
What are some working models that are a fit the formula for the
MRB constant?, URL (version: 2020-01-12):
https://math.stackexchange.com/q/3505694

where η is the Dirichlet eta function. Both should be valid for all z∈C.
.

CMRB

by the Abel-Plana formula.

Google Scholar
MRB constant (CMRB)

5,555,555 digit computation of CMRB
(MRB supercomputer output at 18:50:08 am EDT | Friday, July 3, 2020)
Start time is Fri 19 Jun 2020 22:20:08.
Iterations (iter.) required: 7369998
Will give 3599 time estimates, each more accurate than the previous.
Will stop at 7370752 iterations to ensure precision of around 5583332 decimal
places...
1132544 iter. done in 1.161*10^6 s. Ave. 0.97566iter./s. Should take 87.429 days
or 7.554*10^6s. Finish Tue 15 Sep 2020 08:37:29.

{15.3654,% done.}

MRB supercomputer
Processors: Intel Core i9-9900K (5.0 GHz Turbo) (16-Thread) (8-Core) 3.6
GHz. CPU Boost: Stage 2: Overclock CPU - Up to 5.1GHz on All CPU Cores at
3200 Mhz RAM Extreme Cooling: H20: Stage 2: Corsair H115i PRO - 280mm
Liquid CPU Cooler with the following two exterior nodes: 4.7 GHz on all Intel
6 cores at 3000 MHz RAM and 4 cores of 3.6 GHz at 2400 MHz RAM!

<- by Fubini’s theorem for double series along with->

{

<- by a Taylor expansion of η(s) around s = 0

<- as pointed out by J. Borwein, is the j-th Taylor
co efficient in the expansion of about x = 0.

Try to break these CMRB Computational
Records
(Click for the full amazing ride!)

This conditionally convergent series is transformed
into the following absolutely convergent two by
Richard Crandall (2012).

}

These limits are transformed into the
following infinite series.

Collecting the terms of this series gives us
the following conditionally convergent one.

(η is the Dirichlet eta function.)

Finch, Steven R. (2003). Mathematical
Constants. Cambridge, England: Cambridge
University Press. p. 450. ISBN 0-521-81805-2.

First published in book form by

Gottfried Helms (https://math.stackexchange.com/users/1714/gottfried-helms), MRB constant
proofs wanted, URL (version: 2015-12-24): https://math.stackexchange.com/q/1587347


		CMRB =

	=CMRB

CMRB

Given that C MRB =

The MRB constant is defined at http://mathworld.wolfram.com/MRBConstant.html. After a lot of looking I found a
connection between the MRB constant and applied math:

The MRB constant is ∑(−1)^k(k^(1/k)−1), and that k^(1/k)−1 is the interest rate to multiply an investment k times in
k periods -- as well as other growth models involving the more general expression (1+k)^n --
since ((k^(1/k)−1)+1)^k|k∈Z+=k. and ((k^(1/n)−1)+1)^n|n∈Z+=k.

We can say, the result of summing, with alternating signs, the interest rate to multiply an investment k times in k
periods (or the equivalent growth model) could be the end "growth" rate resulting from growth, following decay,
following growth, ad infinitum.

Since = 3, consider

Notice this real life application.