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Probable bug: EvaluationMonitor with NIntegrate, "ExtrapolatingOscillatory",

• To: mathgroup at smc.vnet.net
• Subject: [mg85684] Probable bug: EvaluationMonitor with NIntegrate, "ExtrapolatingOscillatory",
• From: Andrew Moylan <andrew.j.moylan at gmail.com>
• Date: Tue, 19 Feb 2008 01:58:05 -0500 (EST)

For NIntegrate[BesselJ[0, x^2], {x, 0, Infinity}, EvaluationMonitor :>
bla], EvaluationMonitor is not being called with x set to the actual
values at which the integrand is being evaluated.

To see this:

dummy[x_?NumericQ] := (Sow[x, 1]; 1)
ListPlot /@ (NIntegrate[dummy[x] BesselJ[0, x^2], {x, 0, Infinity},
EvaluationMonitor :> Sow[x, 2]] // Reap // Last)

Presumably the reason for the bug is that method
"ExtrapolatingOscillatory" (which is being used automatically for this
integrand) is (correctly) integrating between the roots of BesselJ[0,
x^2], but EvaluationMonitor is being evaluated with x set to the roots
of BesselJ[0, x], i.e., with x being set to the value of an internal
transformed integration variable.