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Update In a comment Oleksandr pointed out that the number of iterations may be having an effect. This is evident from running the following code: max = 10; qp = Table[Unique[{q, p}], {max}]; qpFlat = Flatten[qp]; eqn = totalenergy[qp, max]; ceqn = Compile[Evaluate[{#, _Real} & /@ qpFlat], Evaluate[eqn], "RuntimeOptions" -> ...


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First of all correcting the sign in the exponential we get f2 = Integrate[ Exp[r^2/(2 M^2)] (b^2 - 3 r^2)^2 (Abs[b^2 + r^2] - (b^2 - r^2))/( r (r^2 - b^2)), {r, 0, I \[Infinity]}, Assumptions -> {M > 0, b > 0] (* Out[278]= 18 b^2 M^2 + 4 b^4 E^(b^2/(2 M^2)) ExpIntegralEi[-(b^2/(2 M^2))] *) Taking the pricipal value has no influence as ...



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