Timeline for Use of AccuracyGoal & MachinePrecision in NIntegrate
Current License: CC BY-SA 3.0
5 events
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| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jun 14, 2016 at 19:03 | comment | added | ConvexMartian | Thank you very much for your thorough comment! I'd be happy to consider this an answer if you feel like submitting it as one. | |
| Jun 14, 2016 at 0:20 | comment | added | J. M.'s missing motivation♦ |
As it turns out, your result is accurate to 34 or so digits when compared to -EulerGamma/2 + π/8 - 3 Log[2]/4 + Log[π]/2. Anyway: Method -> "DoubleExponential" gives good results for integrals like this. A rule of thumb you can use is that you can set AccuracyGoal up to ten less than the WorkingPrecision setting. Thus, you could try SetPrecision[ NIntegrate[(1 - Exp[-x] (1 + x))/(2 x (Exp[x] - 1) Cosh[x]), {x, 0, ∞}, AccuracyGoal -> 35, Method -> "DoubleExponential", WorkingPrecision -> 45], 35].
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| Jun 13, 2016 at 23:41 | history | asked | ConvexMartian | CC BY-SA 3.0 |