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2

I see at least two problems here: As written Prob1 is a List; you need to add // First (or similar) to extract a scalar value. You failed to define a starting value for Sh1 therefore Sh1 = 0 + Sh1 leads to an infinite recursion when the first scalar value is Equal to zero. Additionally some more improvements to be made: You should avoid starting user ...

4

Although BSplineFunction[] is sadly limited to machine precision results, it's not too hard in this case to make a function that will give exact results for exact input. You've already given the control points, so the task is a whole lot easier than the situation in this related answer. Just as in that answer, we use the strategy of starting with ...

5

As the old documentation states: $EqualTolerance gives the number of decimal digits by which two numbers can disagree and still be considered equal according to Equal. The default setting is equal to Log[10, 2^7], corresponding to a tolerance of 7 binary digits. On my system$MachinePrecision is ~15.9546 which means there are 53 bits: ...

2

Using Integrate inside NIntegrate is pointless, since the result is numerical anyways. I'd suggest: \[Theta] = \[Pi]/20; q = 3/10; g = 5/100; v = 5; w = 2/10; Z = 2; int[t_?NumericQ] := NIntegrate[BesselJ[0, x*Sin[\[Theta]]]*Exp[-x*Cos[\[Theta]]],{x, 0, q*v*t}] NIntegrate[int[t]*Exp[-g*t/2]*Cos[w*t]/t, {t, 0, \[Infinity]}, PrecisionGoal -> 12] Specify ...

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