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Apr
25
comment Multiply integrand with -1, and the precision changes?
@Xavier Interesting. Using the code in the update of this answer, I found that in this case NIntegrate internally switches to "LevinRule", and the output is indeed the same as that with option , Method -> "LevinRule". How about giving an answer?
Apr
23
revised Multiply integrand with -1, and the precision changes?
added 262 characters in body
Apr
23
revised Multiply integrand with -1, and the precision changes?
add another example, rephrase the question a little
Apr
23
revised Multiply integrand with -1, and the precision changes?
simplify the sample
Apr
23
comment Multiply integrand with -1, and the precision changes?
@J.M. I also tried manually implement "ExtrapolatingOscillatory", and the problem doesn't show up in my (much slower) implementation: zero[i_] := Piecewise[{{BesselJZero[0, i], i > 0}}];separatepmhankel[p_?NumericQ, sign : 1 | -1, i_?NumericQ, prec_] := NIntegrate[sign ξ BesselJ[0, ξ] f[p, ξ], {ξ, zero@i, zero[i + 1]}, WorkingPrecision -> prec, MaxRecursion -> 40]; manualpmhankel[p_, sign_: 1, prec_: 16] := NSum[separatepmhankel[p, sign, i, prec], {i, 0, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> prec]; manualpmhankel[32, #, 32]&/@{1,-1} // AbsoluteTiming
Apr
23
comment Multiply integrand with -1, and the precision changes?
@Searke Thanks for the response. (1) With "SymbolicProcessing->0" the problem remains: pmhankelTest[p_, sign_: 1, prec_: 16] := NIntegrate[sign ξ BesselJ[0, ξ] f[p, ξ], {ξ, 0, ∞}, WorkingPrecision -> prec, Method -> {"ExtrapolatingOscillatory", "SymbolicProcessing" -> 0}];pmhankelTest[32, #, 32] & /@ {-1, 1} (2) I tried IntegrationMonitor mentioned in this answer, the {"Boundaries", "Dimension", "Error", "GetRule", "Integrand"} etc. seems to be all the same, and the only difference between "Integral" is the sign.
Apr
23
revised Multiply integrand with -1, and the precision changes?
added 82 characters in body
Apr
22
comment Which one is now correct? ArcTan[x] or ArcTan[x,y]?
It's simply because ArcTan[y/x] and ArcTan[x,y] are different, do check the document carefully. If you still have difficulty in understanding the difference, try comparing the results of ArcTan[-1/-1] and ArcTan[-1, -1] and think about the reason.
Apr
22
revised Multiply integrand with -1, and the precision changes?
deleted 12 characters in body
Apr
22
revised Multiply integrand with -1, and the precision changes?
edited tags
Apr
22
revised Multiply integrand with -1, and the precision changes?
added 22 characters in body
Apr
22
revised Numerical inverse Laplace-Hankel transform
Correct mistakes caused by a typo in the paper.
Apr
22
asked Multiply integrand with -1, and the precision changes?
Apr
22
revised Numerical inverse Laplace-Hankel transform
Typo fixed.
Apr
21
asked Numerical inverse Laplace-Hankel transform
Apr
18
revised DSolve breaks when the ordering of independent variables aren't proper?
deleted 2 characters in body
Apr
17
revised DSolve breaks when the ordering of independent variables aren't proper?
added 8 characters in body; edited tags
Apr
16
comment Compute inverse Laplace transform with Integrate
Though not a complete answer, thanks for your effort :)
Apr
15
awarded  Nice Question
Apr
15
comment Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?
@ShutaoTANG Mainly because I'm still in v9 and want to make the post self-contained so not that willing to use LetL etc. in this sample. You can have a look at this post: mathematica.stackexchange.com/a/54874/1871