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- 604

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Yet another post concerning my battle with a family of messy integrals that are standing between me and a scientific publication.

I'm defining a function by

BWdata[q_,c_,n_]:=NIntegrate[\[Beta]*BesselJ[0,q*\[Beta]]*(E^(-I*c*Gamma[n/2]*Pi^(n/2-1)/8*HypergeometricU[n/2,1,\[Beta]^2/4])-1),{\[Beta],0,Infinity},Method->{"ExtrapolatingOscillatory",Method->{"GlobalAdaptive",MaxErrorIncreases->1000}},WorkingPrecision->200,MaxRecursion->30]

For n=6 at q=0 I get the error message:

NIntegrate::inumri: The integrand (-1+E^(-(65/4) I \[Pi]^2 (1/4 (-3+Times[<<2>>])+1/4 E^Times[<<2>>] (2+Power[<<2>>]+Times[<<2>>]) Gamma[0,Times[<<2>>]]))) \[Beta] has evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries {{0.*10^-101,5.230427695955377022882968073746754104809181670112054730607300437187234132398206612751798579662814260*10^7}}. >>

The working precision is so high because I came across this thread in which DaleSpam advised someone receiving the same error message to turn their working precision up. I was originally having problems with n=4 at q=0 as well, and increasing the working precision up to about 80 solved that. However, I'm racheting up my working precision as I type this and I'm having no luck (it's up to 700 as I type this). If I keep increasing it much higher I'm worried that the full set of integrals I have to do will start to take an inordinate amount of time. Does anyone have any other suggestions for things I could try?

The function for q=0 oscillates strongly up to a point and then decays slowly, so I tried using an oscillatory strategy over the appropriate region and then using the default method to try and tackle the rest, but to no avail.

Thanks in advance.