In[]:=
g[x_]=x^(1/x);t=(Timing[t10k=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision10000,Method"Trapezoidal",MaxRecursion13]+I/Pi)])[[1]];​​t
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[]=
3250.55
In[]:=
N[test-t10k,10000]
Out[]=
0.×
-10001
10
+0.×
-10001
10

convert to exponential
0.×
-10001
10
+0.×
-10001
10

Out[]=
0.×
-10001
10
0``-0.49714987269413446

60, 000 18
Syntax::sntxf: 60 cannot be followed by , 000 15.
Out[]=
0
In[]:=
g[x_]=x^(1/x);t=Timing[t10k=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision10000,Method"Trapezoidal",MaxRecursion12]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 12 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 10009+10010 and 10015 for the integral and error estimates.
Out[]=
695.688
In[]:=
N[t10k-test,20]
Out[]=
-7.2038809926161842×
-8278
10
-8.0907465373258423523×
-8275
10

MaxRecursionguide​​​​maxdigitsM.R.1309default​​241010​​445311​​827512​​1544213​​2893214​​5428615​​10260016​​19391417
In[]:=
g[x_]=x^(1/x);t=Timing[t1309=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision1309,Method"Trapezoidal",MaxRecursion9]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 9 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 1317+1318 and 1322 for the integral and error estimates.
Out[]=
2.32813
In[]:=
g[x_]=x^(1/x);t=Timing[t2410=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision2410,Method"Trapezoidal",MaxRecursion10]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 10 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 2418+2419 and 2424 for the integral and error estimates.
Out[]=
13.8906
In[]:=
N[t2410-test,20]
Out[]=
-1.×
-2410
10
-1.03×
-2408
10

In[]:=
g[x_]=x^(1/x);t=Timing[t4453=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision4453,Method"Trapezoidal",MaxRecursion11]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 11 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 4461+4462 and 4466 for the integral and error estimates.
Out[]=
52.75
In[]:=
N[t4453-test,20]
Out[]=
0.×
-4454
10
+2.×
-4453
10

In[]:=
g[x_]=x^(1/x);t=Timing[t8p182k=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision8182,Method"Trapezoidal",MaxRecursion12]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 12 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 8190+8191 and 8196 for the integral and error estimates.
Out[]=
377.328
In[]:=
N[t8p182k-test,20]
Out[]=
0.×
-8183
10
+0.×
-8183
10

In[]:=
g[x_]=x^(1/x);t=Timing[t154424=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision15442,Method"Trapezoidal",MaxRecursion13]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 13 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 15451+15452 and 15457 for the integral and error estimates.
Out[]=
3536.61
In[]:=
N[t154424-test,20]
Out[]=
0.×
-15443
10
-1.×
-15442
10

In[]:=
g[x_]=x^(1/x);t=Timing[t28932=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision28932,Method"Trapezoidal",MaxRecursion14]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 14 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 28941+28942 and 28948 for the integral and error estimates.
Out[]=
17751.6
In[]:=
N[t28932-test,20]
Out[]=
2.×
-28932
10
+1.8333×
-28928
10

In[]:=
g[x_]=x^(1/x);t=Timing[t54286=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision54286,Method"Trapezoidal",MaxRecursion15]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 15 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 54295+54296 and 54302 for the integral and error estimates.
Out[]=
112226.
In[]:=
N[t54286-test,20]
Out[]=
0.×
-54287
10
+0.×
-54287
10

In[]:=
Precision[FM2200K]
Out[]=
199999.
In[]:=
g[x_]=x^(1/x);t=Timing[t250000=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision250000,Method"Trapezoidal",MaxRecursion18]+I/Pi)][[1]];​​t
Out[]=
$Aborted
Out[]=
13.2344
N[t250000-FM2200K,20]
​​​​​​​​​​
In[]:=
g[x_]=x^(1/x);t=Timing[t10k=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision3000,Method"Trapezoidal",MaxRecursion10]+I/Pi)][[1]];​​t
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 10 iterated refinements in t in the region {{0,∞}}. NIntegrate obtained 3008+3009 and 3014 for the integral and error estimates.
Out[]=
13.2344
In[]:=
N[FM2200K=FM2200K-2/PiI]
Out[]=
0.070776-0.684
In[]:=
N[t10k-FM2200K]
Out[]=
0.+0.
In[]:=
g[x_]=x^(1/x);t=Timing[t60k=-(INIntegrate[(g[(1+tI)])/(Exp[Pit]),{t,0,Infinity},WorkingPrecision60000,Method"Trapezoidal",MaxRecursion18]+I/Pi)][[1]];​​t​​
Compare with 40,000