Timeline for Numerical comparison of two integrals and a function :
Current License: CC BY-SA 4.0
13 events
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| May 14, 2020 at 18:07 | history | edited | bambi | CC BY-SA 4.0 |
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| May 7, 2020 at 18:37 | comment | added | imas145 | Let us continue this discussion in chat. | |
| May 7, 2020 at 18:35 | comment | added | bambi | What could be the maximum enough value for which accuracy maintains and is withing limits? | |
| May 7, 2020 at 18:32 | comment | added | imas145 | Because the integrand is extremely bad-behaving. You can’t just get a rough estimate when it oscillates like that, the rough answer is going to be wrong and possibly by a lot. Also, since $\Gamma(x)/x$ grows fast, this oscillation will only get worse as you go to higher values ot $q$. | |
| May 7, 2020 at 18:30 | comment | added | bambi | Why is this issue? Due to wild oscillation? | |
| May 7, 2020 at 18:29 | comment | added | imas145 | Not unless you can properly compute the function values up to $q=10^4$ | |
| May 7, 2020 at 18:26 | comment | added | bambi | Can I get a graph of them three in one axis system for q at least 10^4? You can give it as an answer to me . I just need the rough inter- comparison. | |
| May 7, 2020 at 18:14 | comment | added | imas145 |
Running NIntegrate[Sin[(π Gamma[x])/(2 x)]^2, {x, 2, 10^4}, Method -> "LevinRule", MinRecursion -> 20, MaxRecursion -> 50] gives out an answer without warnings, but I can't really judge its validity.
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| May 7, 2020 at 18:07 | history | edited | J. M.'s missing motivation♦ |
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| May 7, 2020 at 18:07 | comment | added | J. M.'s missing motivation♦ |
Hopefully you are aware that LogIntegral[] is built-in? Additionally: perhaps you could explore using NDSolve[] for your $S(q)$; e.g. sol = NDSolveValue[{s'[q] == Sin[Exp[Log[Pi/2] + LogGamma[q] - Log[q]]]^2, s[2] == 0}, s, {q, 2, 10}].
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| May 7, 2020 at 18:06 | comment | added | imas145 |
Plotting the first integrand shows it's highly oscillatory. Other than throwing (a lot) more precision at it and/or using LevinRule, I can't think of a straight-forward way of efficiently computing it. Maybe someone else can think of a way, but I think your best bet might be to figure out analytically how to make the integrand nicer.
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| May 7, 2020 at 17:44 | history | edited | bambi | CC BY-SA 4.0 |
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| May 7, 2020 at 17:37 | history | asked | bambi | CC BY-SA 4.0 |