Let m be the MRB constant:

In[]:=
MRB constant
Assuming "MRB constant" is referring to a mathematical definition | Use as
a mathematical constant
instead
Input interpretation
MRB constant
Illustration
Definition
Fewer details
Consider the sequence of partial sums defined by
s
n

n
∑
k1
k
(-1)
1/k
k
.
As can be seen in the plot above, the sequence has two limit points at
-0.812140…
and 0.187859… (which are separated by exactly 1). The upper limit point is sometimes known as the MRB constant after the initials of its original investigator (Burns 1999; Plouffe).
Sums for the MRB constant are given by
S
=
lim
N∞
2N
∑
n1
n
(-1)
1/n
n
=
1+
lim
N∞
2N+1
∑
n1
n
(-1)
1/n
n
=
∞
∑
k1
[
1/(2k)
(2k)
-
1/(2k-1)
(2k-1)
]
=
∞
∑
k1
k
(-1)
(
1/k
k
-1)
=
0.1878596424…
(Finch 2003, p. 450; OEIS A037077).
Related terms
Glaisher-Kinkelin constant
|
power tower
|
Steiner’s problem
Subject classifications
Show details
MathWorld
miscellaneous constants

In[]:=
MinkowskiQuestionMark
Input interpretation
MinkowskiQuestionMark (Wolfram Language symbol)
Usage
MinkowskiQuestionMark[x] gives Minkowski's question mark function ?(x).
More information »
Basic examples
Evaluate
MinkowskiQuestionMark
at a quadratic irrational number:
In[1]:=
MinkowskiQuestionMark
3
-1
2

Out[1]=
2
7
Plot
MinkowskiQuestionMark
over the unit interval:
In[1]:=
Plot[MinkowskiQuestionMark[x],{x,0,1}]
Out[1]=
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
Attributes
Listable
|
Protected
|
ReadProtected
Relationships with other entities
Hide relationship communities
Eponymous person
Hermann Minkowski
Related symbols
ContinuedFraction
|
CantorStaircase
Typical ranks of usage in programs
Show more ranks
Frequency of usage in all corpuses
th
4286
most common (1 in 8680000 symbols)
Rank of usage in the Wolfram documentation
th
2940
most common (1 in 94100 symbols)
History
Version introduced or modified
introduced in Version 10 (July 2014)
Timeline
Show release numbers
​​
Is?(exp(πm))rational?
​​​​
In[]:=
m=NSum[
n
(-1)
(
1/n
n
-1),{n,1,Infinity},Method->"AlternatingSigns",WorkingPrecision->10000];
In[]:=
MinkowskiQuestionMark[Exp[mPi]]
Out[]=
1.9376220479634868038140291677221554627858829625719368197542423022194051029567602158139178323882659080726196637085387438313721641947040552622638642787933349609375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000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00000000000000000000000000000000000000000000000000000000000000000000000000000000000000

In[]:=
1.9376220479634868038140291677221554627858829625719368197542423022194051029567602158139178323882659080726196637085387438313721641947040552622638642787933349609375