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The Package HypExp does exactly that. Here is the link to paper for what I believe was the last extension. After digging around a bit, the package files should be available here ( Edit freely available link) Several years ago, there has been some work on the simplification of polylogarithms into a Hopt Algebras, which simplifies the reduction of the ...


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Vladimir, there is one simple solution: lst = Table[{a, NIntegrate[BesselJ[0, x - a] BesselJ[0,x + a], {x, -\[Infinity], \[Infinity]}, PrecisionGoal -> 5, Compiled -> True]}, {a, 0.84, 0.85, 0.0001}] This visualizes the result: ListPlot[lst, Frame -> True, FrameLabel -> {Style["a", 16], Style["Integral", 16]}, GridLines -> ...


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If you want to evaluate ChebyshevT polynomials accurately you can consider using the Chebyshev recurrence, using memoization. T[0,x_]:=1; T[1,x_]:=x; T[n_,x_]:= T[n,x]=2*x*T[n-1,x]-T[n-2,x]; This should be fast and stable. If you are doing a lot of these, rearranging the computation working from the low index upward would make memoization unnecessary. ...


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LaplaceTransform attempts a symbolic evaluation of the transform, which Mathematica fails to do in this case. To get an answer, write the transform explicitly as an NIntegrate multiple integral. It still takes a while, but reducing the accuracy/precision demands will speed things up: chat = NIntegrate[ GumExpExp Exp[-Ab[s] x - Ar[s] y], {x, 0, ...



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