Marvin Ray Burns

I see how to draw the tessera...

Commented: Marvin Ray Burns 550

May 26 2012

I see how to draw the tesseract and penteract in 2 or 3 dimensions. The graph gets pretty crowded for the penteract. I don't see how I can use an individual edge of graphs of the hexeract and so on. I wonder if the default volume of an n-cube graph in Maple is n units. (That would be convenient.)

with(GraphTheory): with(SpecialGraphs): H4 := HypercubeGraph(4): H5 := HypercubeGraph(5):

Digits := 23Let c be the MRB constantc...

Commented: Marvin Ray Burns 550

May 26 2012

Digits := 23

Let c be the MRB constant

c := .187859642462067120248517934054273230055903094900139

Let C be Catalan's Constant.

C := .9159655941772190150546035149323841107741493742816721

evalf(-(119/19)*C-115+(479561360045/59753497176)*Pi+(525/76)*Pi^2+(102/19)*Pi*ln(2)+(353/76)*Pi*ln(3)-2*c) = -8.*10^(-21)

Digits:=24

c := .187859642462067120248517934054273230055903094900139

evalf((2/7163)*(-90155*e-29388+37921*e^2)/(e*Pi)-c) = -5.19*10^(-22)

evalf(((1325323718/907073065)*Pi-4)/Pi-c) = -2.6*10^(-22)

Again let c be the MRB constant an...

Commented: Marvin Ray Burns 550

May 25 2012

Digits:=22

Again let c be the MRB constant and this time let b be the probability that at least two people in a room of 23 share birthday.

b:=.5072972343239854072254172283370325002359718452929878
c:= 0.187859642462067120248517934054273230055903094900139

(6200 b-239)/(2 (1550 b+437))-1 =0.187859642462067125421

(5 (1860 b+127))/(2 (1550 b+437))-2 =0.187859642462067125421

(5 (4960 b+1001))/(2 (1550 b+437))-7 = 0.187859642462067125421

0.187859642462067125421-c = 5.1725*10^(-18)

Also

evalf(23212425209 /3144920904*Pi-23 - c) = 2.*10^(-20)

and

evalf(20561436223 /2375900782*Pi-27 - c) = 3.*10^(-20)

Also

evalf((-216+53*Pi^(1/2)+363*Pi+1526*Pi^(3/2)+1062*Pi^2)/(92*Pi)-69-c) = -3.*10^(-20)

and

evalf(1/890*(115850*Zeta(3)+10010*Zeta(5)-1785*Pi^2-979*Pi^4)-41-c) = -5.*10^(-20)

and

evalf((6/11)*Pi*arccosh(292945824/1726159)^2-58-c) = 6.*10^(-20)

marvinrayburns.com

Below we have approximations involving t...

Commented: Marvin Ray Burns 550

May 24 2012

Below we have approximations involving the MRB constant. The MRB constant plus a fraction is saved as P while a combination of another constant is saved as Q. We then subtract Q from P and always have a very small result.

Let

Let c be the MRB constant, 0.1878596424620671202485179340542732300559030949001387.

P:= c+7/47

Let G be Graham's Biggest Little Hexagon area.

G:=0.6749814429301047036884958318514002889802977322780266

Q:=(79-940*G)/(3530*G-4032)

p-Q= -3.3803*10^(-18)

P := c+9/46

Let Q be the positive root of 41309050*x^3-2330137

Q:=0.3835118163751105434087

P-Q=5.51007*10^(-17)

P:=c+46/47

Let p be the plastic constant.

p:=1.3247179572447460259609088544780973407344040569017333

Q:=-5*(37*p-2196)/(7000*p-71)

p-Q=6.97*10^(-19)

P:=c+35/48

e:=evalf(exp(1))

Q:= -17(e-5)*(5*e-6)/(-751+215*e+66*e^2)

P-Q= -1.710*10^(-19)

P:=c+40/49

Let r be the rabbit constant

r:=0.7098034428612913146417873994445755970125022057678605

Q:=6*(167*r+1060)/(25*r+7024)

P-Q= -1.20*10^(-19)

P:=c+29/51

Let Pg be plouffe's gamma constant.

Pg:=0.1475836176504332741754010762247405259511345238869178

Q:=-20*(303Pg-40)/(178Pg-151)

P-Q=-1.12336*10^(-17)

P:=c+15/17

Let F be the Fransén-Robinson Constant,

F:=2.8077702420285193652215011865577729323080859209301982

Q:=(20882-2007*F)/(1050 + 4700*F)

P-Q= -1.739*10^(-18)

P:=c+37/52

Let QRS be the QRS constant.

QRS:=0.6054436571967327494789228424472074752208994969563226

Q:=(3970*QRS+83)/(6053*QRS-900)

P-Q=1.7719*10^(-18)

P:=c+43/52

Let f1 be the first Foias constant.

f1:=2.2931662874118610315080282912508058643722572903271212

Q:=(3881-220*f1)/(100*f1+3098)

P-Q= -3.670*10^(-18)

P:=c+16/53

Let Pa be Plouffe's A constant

Pa:=0.1591549430918953357688837633725143620344596457404564

Q:=4*(5800Pa-773)/(6000Pa+271)

P-Q=4.6241*10^(-18)

This post is continued in the MRB consta...

Commented: Marvin Ray Burns 550

May 21 2012

This post is continued in the MRB constant N Part 3.

...

Commented: Marvin Ray Burns 550

May 13 2012

(1)

Again let b be

(2)

Then we have the divergent series

evalf(sum((-1)^n*(-b*n^(1/n)-b), n = 1 .. infinity))

(3)

That is MRB constant times b plus 1

>

(4)

We also have the convergent series

evalf(sum((-1)^n*(b*n^(1/n)-b), n = 1 .. infinity))

(5)

That is obviously MRB constant times b:

>

(6)

That means that we have the following equations.

evalf(sum((-1)^n*(-b*n^(1/n)-b), n = 1 .. infinity)-(sum((-1)^n*(b*n^(1/n)-b), n = 1 .. infinity)))

(7)

evalf(sum((-1)^n*(-b*n^(1/n)-b-b*n^(1/n)+b), n = 1 .. infinity))

(8)

evalf(sum((-1)^n*(-b*n^(1/n)-b*n^(1/n)), n = 1 .. infinity))

(9)

evalf(sum((-1)^n*(-2*b*n^(1/n)), n = 1 .. infinity))

(10)

evalf(-2*(sum((-1)^n*b*n^(1/n), n = 1 .. infinity)))

(11)

evalf(sum((-1)^n*b*n^(1/n), n = 1 .. infinity))

(12)

Finally, as we saw in the original post, we have the following.

evalf(sum(-(-1)^n*b*n^(1/n), n = 1 .. infinity))

(13)

evalf(-b*(sum((-1)^n*n^(1/n), n = 1 .. infinity)))

(14)

But sum((-1)^n*n^(1/n), n = 1 .. infinity) ia a divergent series whoes Cesàro summation is MRB constant -1/2

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

(15)

So -b times (MRB constant -1/2) =1/2:

(16)

Thus b times (1/2-MRB constant) =1/2:

(17)

Therefore b*MRB constant=(b-1)*1/2:

(18)

Download May122012d.mw

> ...

Commented: Marvin Ray Burns 550

May 06 2012

In other words, is the series that is made from the sum of those two divergent series absolutely convergent?

Download cincodemayo2012.mw

For a few x that I have tried a is solve...

Commented: Marvin Ray Burns 550

April 29 2012

For a few x that I have tried, a is solved for in $sum((-1)^n*(a*n^(1/n)-a), n = 1 .. infinity)$ =x when a= $x/MRB constant$ .

Maple confirms this by the following:

All Convergent Series?...

Commented: Marvin Ray Burns 550

April 22 2012

@icegood

I wonder if the Cesàro mean is faster than the partial sums to converge for all convergent series? I also wonder if it is true that Levin's u-transform is better than all the Cesàro transforms for computing the MRB constant is it indeed better for summing all convergent series?

About Levin's u-transform Mathematica (using Nsum[,"AlternatingSigns"]) sums the MRB constant a magnitude of times faster than Maple(using evalf(sum)); Mathematica might use a diffferent method.

See http://www.mapleprimes.com/posts/95240-Computing-Digits-Of-The-MRB-Constant

The Chezaro mean seems to converge ...

Commented: Marvin Ray Burns 550

April 21 2012

For this series the Cesàro mean seems to converge faster than the partial sums.

Download mran.mw

Previously we had the funct...

Commented: Marvin Ray Burns 550

April 16 2012

Download 4162012.mw

x^x^x^x...

Commented: Marvin Ray Burns 550

January 21 2012

Download 1212012b.mw

Download 1212012c.mw

marvinrayburns.com

For some -.38<x<-.18 (x^x^x^x) has...

Commented: Marvin Ray Burns 550

January 14 2012

For some -.38 < x < -.18, (x^x^x^x) has a large magnitude. (It has real and imaginary parts far from 0 in either the positive or negative direction.) Then x^(x^x^x^x) is very close to 0.