# How to calculate the following integral of the multiplication of two Bessel functions?

This integration has an analytical solution and its behavior is described by 1/r^2 function, but Mathematica gives some weird oscillating answer. Can anybody explain this and help me overcome this issue.

R  = 1500;
f[r_] := NIntegrate[BesselJ[2, r*k]*BesselJ[1, R*k], {k, 0, Infinity},AccuracyGoal -> 12]
sol = Table[Abs[f[r]]^2, {r, R, 2000, 10}];
ListLinePlot[sol, PlotRange -> All]

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Integrate[BesselJ[2, pk]*BesselJ[1, Rk], {k, 0, Infinity}, Assumptions -> p > R] – Dr. belisarius Mar 20 '14 at 16:10
Numerically R = 1500; f[r_] := NIntegrate[BesselJ[2, r*k]*BesselJ[1, R*k], {k, 0, Infinity}] sol = Table[Abs[f[r]]^2, {r, R, 2000, 10}]; ListLinePlot[sol, PlotRange -> All] – Dr. belisarius Mar 20 '14 at 16:12

## 1 Answer

R = 1500;
f[r_] := NIntegrate[BesselJ[2, r*k]*BesselJ[1, R*k], {k, 0, Infinity}]
sol = Table[Abs[f[r]]^2, {r, R, 2000, 10}];
ListLinePlot[sol, PlotRange -> All]


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Hi. So the problem was the AccuracyGoal? Why? Also, I get a warning NIntegrate::ncvb while calculating this. – artalexan Mar 20 '14 at 16:32
@artalexan I'mon version 9, and NIntegrate doesn't show any warning. Perhaps a version or configuration mismatch – Dr. belisarius Mar 20 '14 at 17:34