# ExtrapolatingOscillatory integration strategy in Mathematica

1. Sep 5, 2012

### muppet

"ExtrapolatingOscillatory" integration strategy in Mathematica

A question I can't work out from the "advanced numerical integration" documentation for Mathematica. In http://reference.wolfram.com/mathematica/tutorial/NIntegrateIntegrationStrategies.html it claims that Mathematica recognises oscillatory kernels of certain common forms (e.g. trig and Bessel functions), integrates from one zero of the oscillatory function to the next, and uses an algorithm to accelerate the convergence of the resulting alternating series.

Those who help on this or the programming subforum a lot will know I'm dealing with some integrals of the form
$$\int^{\infty}_0 db b J_0 (bq)(e^{i f(b)}-1)$$

Can anybody tell me what Mathematica will do, given the "Extrapolating Oscillatory" strategy, with this integrand that has two oscillatory products?