WOLFRAM NOTEBOOK

In[]:=
Timing[CMRB=NSum[(-1)^n(n^(1/n)-1),{n,1,Infinity},WorkingPrecision200,Method"AlternatingSigns"]]​​
Out[]=
{0.15625,0.187859642462067120248517934054273230055903094900138786172004684089477231564660213703296654433107496903842345856258019061231370094759226630438929348896184120837336626081613602738126379373435283224982}
In[]:=
Precision[MKB]
Out[]=
99999.8
In[]:=
FMKB[prec_,MR_]:=Module[{},g[x_]=N[Log[x]/x,prec+5];​​t[prec]=Timing[MKB-(-(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec+5,PrecisionGoalprec+5,Method"Trapezoidal",MaxRecursionMR])+I/Pi)];N[t[prec],prec]]​​
In[]:=
FMKB[1000,9]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 9 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 1013+1014 and 1017 for the integral and error estimates.
Out[]=
{1.75,0.×
-1006
10
+0.×
-1006
10
}
In[]:=
ClearSystemCache[];prec=2000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion10]-I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 10 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 2008+2009 and 2014 for the integral and error estimates.
Out[]=
{10.9844,0.×
-2001
10
+0.×
-2001
10
}
In[]:=
ClearSystemCache[];prec=3000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion11]-I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 11 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 3008+3009 and 3014 for the integral and error estimates.
Out[]=
{45.5625,0.×
-3001
10
+0.×
-3001
10
}
In[]:=
ClearSystemCache[];prec=4000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion11]-I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 11 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 4008+4009 and 4014 for the integral and error estimates.
Out[]=
{80.0313,0.×
-4001
10
+0.×
-4001
10
}
In[]:=
ClearSystemCache[];prec=5000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion12]-I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 12 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 5008+5009 and 5014 for the integral and error estimates.
Out[]=
{236.125,0.×
-5001
10
+0.×
-5001
10
}
In[]:=
ClearSystemCache[];prec=10000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion13]-I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 13 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 10009+10010 and 10015 for the integral and error estimates.
Out[]=
{1802.72,0.×
-10001
10
+0.×
-10001
10
}
In[]:=
ClearSystemCache[];prec=40000;g[x_]:=N[Log[x]/x,prec];Timing[MKB--(INIntegrate[Exp[-Pit+g[1+tI]],{t,0,Infinity},WorkingPrecisionprec,​​Method"Trapezoidal",MaxRecursion15]-I/Pi)]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 15 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 40009+40010 and 40016 for the integral and error estimates.
Out[]=
{92496.8,0.×
-40001
10
+0.×
-40001
10
}
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