MaxRecursion(/WorkingPrecision?) Error in Mathematica 8

[muppet]

I'm getting an error message that suggests my attempts to increase the variable MaxRecursion in NIntegrate aren't working.

I define
f[n_,b_]:=NIntegrate[q*BesselJ[0,q*b]*(-(2/(n (2+n) q^4))+(1-q^2)^(n/2) HeavisideTheta[1-q^2] ((2+n q^2)/(n (2+n) q^4)-Hypergeometric2F1[1,n/2,1+n/2,1-1/q^2]/(n q^2))),{q,0,Infinity},Method->"DoubleExponentialOscillatory",MaxRecursion->50,WorkingPrecision->30]

and upon trying to evaluate f[3,4] I get the message
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in q near {q} = {1.00125749138406369739184946806}. NIntegrate obtained 0.0302818978835504820230915378392`30. and 1.04354107472455181267006501674`30.*^-16 for the integral and error estimates. >>
9 being the default value of MaxRecursion.

Does anyone have any ideas why?
I'm also finding that when I try and

Plot[f[3,b],{b,0,1},WorkingPrecision->30]

I'm getting the message
NIntegrate::precw: The precision of the argument function (q BesselJ[0,0.0000204286 q] (-(2/(15 q^4))+(1-q^2)^(3/2) ((2+3 Power[<<2>>])/(15 q^4)-(-1+1/q^2+Power[<<2>>] ArcTanh[<<1>>])/((1+Times[<<2>>])^2 q^2)) HeavisideTheta[1-q^2])) is less than WorkingPrecision (30.`). >>

How do I fix this?

Thanks in advance.

 

[mmwave]

it is important to troubleshoot and solve any issues that arise in our experiments or calculations. In this case, it seems like there may be some issue with the integration method and the precision settings.

Firstly, it is worth checking if the function being integrated is well-behaved and if the integration limits are appropriate. This could cause convergence issues and could be the reason for the error message.

Another potential solution could be to try different integration methods, such as the "GlobalAdaptive" or "MonteCarlo" methods. Sometimes, different methods can give better results for certain integrals.

It is also important to note that increasing the MaxRecursion value may not always improve the accuracy of the integral. In some cases, it may lead to an infinite loop or take a very long time to compute.

Regarding the second issue with the precision, it may be helpful to try increasing the WorkingPrecision value to see if that resolves the issue. It could also be worth checking if there are any issues with the function being plotted or the range of values being used.

In summary, troubleshooting integration errors can be a trial-and-error process, and it may require trying different methods and adjusting precision settings. It is also helpful to carefully check the input function and integration limits to ensure they are appropriate for the problem at hand.