Reduce a MeijerG to elementary function

Question

The following function for $t>0$

f[t_]:=1/(8 (-1+E^(2 t)) \[Pi]^(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])

is actually an elementary function, by

Plot[Evaluate[4Exp[4t]f[t]],{t,0,1},WorkingPrecision->20]

but FunctionExpand can not simplify it,

FunctionExpand[f[t],Assumptions->t>0]

Mathematica will automatically abort the evaluation. Using

AbortProtect@Trace@FunctionExpand[f[t],Assumptions->t>0]

we can trace the intermediate steps, but I didn't get some useful information from that.

Is there some other way to deal with MeijerG functions (if not for Mathematica, is there some useful Python package for this?)

Answer 1

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    *)