In[]:=
N[(Timing[FM2200K-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->200000,Method->"Trapezoidal",MaxRecursion->17]+I/Pi)]),20]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 17 iterated refinements in t in the region {{1.`200000,∞}}. NIntegrate obtained 200011-200010 and 200018 for the integral and error estimates.
Out[]=
{6.96097×
6
10
,0.×
-189330
10
+2.4246298580811754111×
-166700
10
}
MKB=
∞
∫
1
exp(πt)(
1/t
t
-1)t
∞
∫
1
(
1/t
t
-1)exp(πt)t
∞
∫
1
exp(πt)
log(t)
t

-1t
Now, since
πt

log(t)
t


log(t)
t
-
πt


MKB=
∞
∫
1
exp
log(t)
t
-
πt

t+C.
In[]:=
6.960970046875`*^6/3600
Out[]=
1933.6
In[]:=
%/24
Out[]=
80.5668
In[]:=
N[FM2200K]
Out[]=
0.070776-0.684
In[]:=
In[]:=
FM2200K//N
Out[]=
0.070776-0.0473806
In[]:=
Precision[FM2200K]
Out[]=
199999.