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Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

1
vote
Another approach if you want to avoid the use of AsymptoticIntegrate (whose very presence I learnt today, thanks @Roman:-)!). Timing[ FullSimplify[ Integrate[(y (1 - x)^2 (1 + x))/(x + (1 - x^2) y …
answered May 1 by Dimitris
1
vote
I think this is not a answer but can serve as a summary of the useful workarounds. Still we do not have a rigorous explanation of the buggy (?) behavior. Since Integrate[BesselJ[0, x], {x, 0, \[Infi …
answered Oct 16 '15 by Dimitris
2
votes
I don't see any any particular reason why the integral should be real. chi = 62/27; phi[x_] := x Log[x] + (1 - x) Log[1 - x] + chi x (1 - x) integrand = phi[x] Log[phi[x]] + (1 - phi[x]) Log[1 - …
answered Feb 27 '17 by Dimitris
2
votes
Just a workaround. In[4]:= Clear["Global`*"] In[5]:= f[x_, t_] := Abs[Re[Exp[I*x]/(1 - t*Exp[I*x])]] In[6]:= Timing[ resAn[t_] = Integrate[f[x, EulerGamma], {x, 0, 2*Pi}] /. EulerGamma -> t] O …
answered Nov 18 '14 by Dimitris
1
vote
(Mathematica 10) Numerically: Needs["NumericalCalculus`"] NLimit[Power[Sqrt[((1 - 4 n)/(3 n + 2))^(3 n)]^2, (n)^-1], n -> ∞] // Chop // Rationalize[#, .000001] & (* 64/27 *) Symbolically Lim …
answered Apr 8 '17 by Dimitris
5
votes
If you are sure about your integral's behavior you can try Integrate[Exp[I z] 1/z, {z, -Infinity, Infinity}, GenerateConditions -> False] (* I π *)
answered Feb 27 by Dimitris
2
votes
I guess this is a problem of version 9.0. In Mathematica 10 I get the correct result: expr = -((E^(2 n x μ) (-1 + Gamma[2, n x μ]) (λR^2))/((λR^2 + (E^(n x μ) ((n μ - λR^2)))))^2) (n μ E^( …
answered Feb 21 '17 by Dimitris
5
votes
1answer
Version 11 Edit The issue still remains: Integrate[BesselJ[0, x], {x, 0, ∞}] // Timing (* {29.8125, 1} *) $Version (* "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" *) Original post …
asked Oct 15 '15 by Dimitris
4
votes
0answers
I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ConditionalExpression[1, Re[m] > -1] Integrate[BesselJ[2 m, x], {x, 0, ∞ …
asked Oct 16 '15 by Dimitris