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tchronis
tchronis
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I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

A solution is to increase WorkingPrecision in Plot:

Plot[CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x], {x, 0, 30}, 
 WorkingPrecision -> 50, PlotRange -> {{0, 30}, {-1, 1}}]

enter image description here

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z]Log[z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := chi[x]N[chi[x] Sinh[x] - shi[x] Cosh[x],50]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_], := 
 EulerGammaWorkingPrecision +-> Log[1050, z] + NIntegrate[(Cosh[t]PlotRange - 1)/t,> {t, {0, z30}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0-1, z1}]}]]

and I got the same figureIt is a little bit slow but it works.

To check special values you can also use CoshIntegral Evaluation to verify the correctness for chi function above.

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure.

To check special values you can also use CoshIntegral Evaluation to verify the correctness for chi function above.

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

A solution is to increase WorkingPrecision in Plot:

Plot[CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x], {x, 0, 30}, 
 WorkingPrecision -> 50, PlotRange -> {{0, 30}, {-1, 1}}]

enter image description here

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := N[chi[x] Sinh[x] - shi[x] Cosh[x],50]

And Plot it:

Plot[res[x], {x, 0, 30},  
 WorkingPrecision -> 50, PlotRange -> {{0, 30}, {-1, 1}}]]

It is a little bit slow but it works.

To check special values you can also use CoshIntegral Evaluation to verify the correctness for chi function above.

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tchronis
tchronis
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I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure.

To check special values you can also use CoshIntegral Evaluation to verify the correctness for chi function above.

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure.

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure.

To check special values you can also use CoshIntegral Evaluation to verify the correctness for chi function above.

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Source Link
tchronis
tchronis
  • 2.4k
  • 1
  • 16
  • 26

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define red[x]res[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure. So probably there is a bug in the CoshIntegral or-and SinhIntegral

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define red[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure. So probably there is a bug in the CoshIntegral or-and SinhIntegral

I verified this behavior. I tried to increase $MaxExtraPrecision but I didn't get any improvement.

At last I created Cosh and Sinh integrals below with increased WorkingPrecision inside NIntegrate.

chi[z_] := N[EulerGamma + Log[10, z] + 
             NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}, WorkingPrecision -> 50], 50]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}, WorkingPrecision -> 50]

Then we can define res[x] as:

res[x_] := chi[x] Sinh[x] - shi[x] Cosh[x]

And Plot it:

Plot[res[x], {x, 0, 30}]

enter image description here

It is a little bit slow but I think it works.

Then i tried with default WorkingPrecision

chi[z_] := EulerGamma + Log[10, z] + NIntegrate[(Cosh[t] - 1)/t, {t, 0, z}]

shi[z_] := NIntegrate[Sinh[t]/t, {t, 0, z}]

and I got the same figure.

Fixed formatting
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edit approved Dec 13, 2013 at 11:56
Öskå
edit approved Dec 13, 2013 at 11:56
Öskå
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added 276 characters in body
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tchronis
tchronis
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Source Link
tchronis
tchronis
  • 2.4k
  • 1
  • 16
  • 26