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deleted 4 characters in body

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edited Mar 22, 2023 at 9:41

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It looks like Mathematica is not trying any of the known transformations of the Meijer G-functions.

We can use the second formula on this Wolfram Functions page,

f[t_] = 1/(8 (-1 + E^(2 t)) π^(3/2)) E^t (
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(5 t)), 1/2] +
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(5 t), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(3 t)), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(3 t), 1/2]);

f[t] /. MeijerG[a_, b_, z_, r_] :> MeijerG[1 - b, 1 - a, 1/z, r] //
  FullSimplify[#, 0 < t <> 1]0] &

(*    E^(-4 t)/4    *)

It looks like Mathematica is not trying any of the known transformations of the Meijer G-functions.

We can use the second formula on this Wolfram Functions page,

f[t_] = 1/(8 (-1 + E^(2 t)) π^(3/2)) E^t (
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(5 t)), 1/2] +
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(5 t), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(3 t)), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(3 t), 1/2]);

f[t] /. MeijerG[a_, b_, z_, r_] :> MeijerG[1 - b, 1 - a, 1/z, r] //
  FullSimplify[#, 0 < t < 1] &

(*    E^(-4 t)/4    *)

It looks like Mathematica is not trying any of the known transformations of the Meijer G-functions.

We can use the second formula on this Wolfram Functions page,

f[t_] = 1/(8 (-1 + E^(2 t)) π^(3/2)) E^t (
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(5 t)), 1/2] +
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(5 t), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(3 t)), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(3 t), 1/2]);

f[t] /. MeijerG[a_, b_, z_, r_] :> MeijerG[1 - b, 1 - a, 1/z, r] //
  FullSimplify[#, t > 0] &

(*    E^(-4 t)/4    *)

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created Mar 22, 2023 at 9:12

Roman

49.8k
2
57
131

It looks like Mathematica is not trying any of the known transformations of the Meijer G-functions.

We can use the second formula on this Wolfram Functions page,

f[t_] = 1/(8 (-1 + E^(2 t)) π^(3/2)) E^t (
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(5 t)), 1/2] +
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(5 t), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, -((2 I)/(3 t)), 1/2] - 
  MeijerG[{{1/2, 1, 3/2}, {}}, {{3/2}, {}}, (2 I)/(3 t), 1/2]);

f[t] /. MeijerG[a_, b_, z_, r_] :> MeijerG[1 - b, 1 - a, 1/z, r] //
  FullSimplify[#, 0 < t < 1] &

(*    E^(-4 t)/4    *)