How I found 2-
13
3CMRBE
​​≃0.00,000,000,02​and
13
3CMRB
+
10
-1
cos
λ

10

7561π
-2
​≃0.00,000,000,000,000,02
Found that Pi=
6ζ(2)
.Then examined
6

MRB
.Found it is approximately
21/26
2

.Then guided Mathematica into finding out that
13/8
(3CMRBE)
≃2, i.e.,​
13
3CMRBE
≃1.9999999997462251
.Found 1.9999999997462251≃
2-
5
ℋ
10
7561
≃2-
10
-1
cos
λ

10

7561π
.​​From
acombination
of those approximations I found:
3(CMRB+r)-
8/13
2
r
π
≃.00000000000000000000502
where r= =
1327c+6
20(187c+4)
and c==
∞
∫
0
Log[1+t]
-1+
t

t
.​

In[]:=
3.141592653589
Input interpretation
3.141592653589
Number line
2.5
3.0
3.5
4.0
Rational form
3141592653589
1000000000000
= 3 +
141592653589
1000000000000
Number name
three point one four one five nine two six five three five eight nine
Continued fraction
Fraction form
[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 2]
Possible closed forms
More
π≈3.14159265358979323
6ζ(2)
≈3.14159265358979323
-1
cos
-
10

Wad
3
≈3.14159265358979323
ζ(2) is zeta of 2 »
cos^(-1)(x) is the inverse cosine function »
W_Wad is the Wadsworth constant

In[]:=
MRB constnat
Assuming "MRB constnat" is a mathematical constant | Use as
referring to a mathematical definition
instead
Input
MRB constant
More information »
Decimal approximation
More digits
0.1878596424620671202485179340542732300559030949001387861720046840…
Number line
0.14
0.16
0.18
0.20
0.22
0.24
Continued fraction
More terms
Fraction form
[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, …]
In[]:=
CMRB=0.187859642462067120248517934054273230055903094900138786172004684
Out[]=
0.18785964246206712024851793405427323005590309490013878617200468
In[]:=
Sqrt[6*CMRB]
Out[]=
1.06167690696011784425556739456273027970600503880017403104590761

In[]:=
1.06167690696
Input interpretation
1.06167690696
Number line
0.8
0.9
1.0
1.1
1.2
1.3
Rational form
13270961337
12500000000
= 1 +
770961337
12500000000
Number name
one point zero six one six seven six nine zero six nine six
Continued fraction
Fraction form
[1; 16, 4, 1, 2, 6, 2, 1, 17, 1, 3]
Possible closed forms
More
6

MRB
≈1.0616769069601178
21/26
2

≈1.0616769070015
1
104
(7ζ(3)+102)≈1.061676906943434
C_MRB is the MRB constant »
ζ(s) is the Riemann zeta function »
In[]:=
6CMRB-2^(21/13)/E
Out[]=
-8.801364971397235293683902073831910352859892318361586×
-11
10
In[]:=
3CMRB-2^(8/13)/E
Out[]=
-4.400682485698617646841951036915955176429946159180793×
-11
10
In[]:=
N[2^(8/13)/(3E),20]
Out[]=
0.18785964247673606187
In[]:=
CMRB-2^(8/13)/(3E)
Out[]=
-1.466894161899539215613983678971985058809982053060264×
-11
10
In[]:=
13/8
(3CMRBE)
Out[]=
1.9999999997462251091717290341558057223094750587247134808008177
In[]:=
13
3CMRBE
-2

In[]:=
1.9999999997462251

There is the possibility of being too greedy for precision. I wonder I was so in if the following.


In[]:=
0.3495591344299050639041087

Here, I recognize: