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MsMath
MsMath
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How can I ask Mathematica to check whethergive the given expression isexplicit real form of the given function?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, now we are sure that it is real). How can I ask Mathematica to checksimplify this expression and give its explicit real form?

How can I ask Mathematica to check whether the given expression is real?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real. How can I ask Mathematica to check this?

How can I ask Mathematica to give the explicit real form of the given function?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, now we are sure that it is real). How can I ask Mathematica to simplify this expression and give its explicit real form?

Source Link
MsMath
MsMath
  • 195
  • 6

How can I ask Mathematica to check whether the given expression is real?

In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real. How can I ask Mathematica to check this?

exp=1/96 (\[Pi]^2 + 
   12 I ArcCos[-(5/4)] ArcTanh[
     1/3 Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] + 
   20 \[Pi]^2 Cosh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] + 
   6 I ArcCos[-(5/4)] Log[2] - 
   12 ArcTanh[
     1/3 Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[
     2] + 3 Log[2]^2 - 
   12 Cosh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] Log[
     2]^2 - 12 I \[Pi] Cosh[
     1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] Log[4] - 
   6 I ArcCos[-(5/4)] Log[9] + 
   12 I ArcCos[-(5/4)] Cosh[
     1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] Log[16] + 
   12 ArcTanh[
     3 Coth[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[
     1 - I Sqrt[15]] - 
   48 I ArcCos[
     I Sqrt[2/3]
       Sinh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Cosh[
     1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] Log[
     1 - I Sqrt[15]] - 
   12 ArcTanh[
     3 Coth[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[
     1 + I Sqrt[15]] + 
   48 I ArcCos[
     I Sqrt[2/3]
       Sinh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Cosh[
     1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] Log[
     1 + I Sqrt[15]] + 
   6 I ArcCos[-(5/4)] Log[I/(
     2 Sqrt[(I + Sqrt[15])/(3 I - 3 Sqrt[15])])] + 
   12 ArcTanh[
     3 Coth[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[I/(
     2 Sqrt[(I + Sqrt[15])/(3 I - 3 Sqrt[15])])] - 
   12 ArcTanh[
     1/3 Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[
     I/(2 Sqrt[(I + Sqrt[15])/(3 I - 3 Sqrt[15])])] + 
   6 I ArcCos[-(5/4)] Log[I/(
     2 Sqrt[(I - Sqrt[15])/(3 I + 3 Sqrt[15])])] - 
   12 ArcTanh[
     3 Coth[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[I/(
     2 Sqrt[(I - Sqrt[15])/(3 I + 3 Sqrt[15])])] + 
   12 ArcTanh[
     1/3 Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[
     I/(2 Sqrt[(I - Sqrt[15])/(3 I + 3 Sqrt[15])])] - 
   6 I ArcCos[-(5/4)] Log[(-1 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(-3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])] + 
   12 ArcTanh[
     1/3 Tanh[
       1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[(-1 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(-3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])] - 
   6 I ArcCos[-(5/4)] Log[(
     1 + Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(-3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])] - 
   12 ArcTanh[
     1/3 Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])]] Log[(
     1 + Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(-3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])] + 
   6 Log[2] Log[(
     3 + Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(-3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])] + 
   3 Log[(3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(-3 + 
      Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])]^2 - 
   48 Cosh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])] PolyLog[
     2, -(1/2)] + 
   6 PolyLog[
     2, -((-3 + 
       Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(
      2 (3 + Tanh[
          1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])))] + 
   6 PolyLog[
     2, -((3 + 
       Tanh[1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])/(
      2 (-3 + Tanh[
          1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])])))]) Sech[
  1/2 (Log[1 - I Sqrt[15]] - Log[1 + I Sqrt[15]])];