# convert MeijerG to form Standard Functions in Mathematica

I'd like to convert

MeijerG[{{}, {1., 1.}}, {{0., 0., 4.}, {}}, -1. T λ]


to its Standard Functions (For example Bessel function or ...). Any suggestion?

From the documentation on MeijerG,

Use FunctionExpand to expand MeijerG into simpler functions:

FunctionExpand@
MeijerG[{{}, {1, 1}}, {{0, 0, 4}, {}}, -T λ]

(* -11 + 11 E^(T λ) + 6 EulerGamma -
5 E^(T λ) T λ + E^(T λ) T^2 λ^2 +
6 (11/6 - EulerGamma - Log[-T λ]) + 6 Log[-T λ] +
6 (-ExpIntegralEi[T λ] - Log[-T λ] +
1/2 (-Log[1/(T λ)] + Log[T λ])) *)


Note this doesn't work if you use floats instead of integers,

FunctionExpand@
MeijerG[{{}, {1., 1.}}, {{0., 0., 4.}, {}}, -1.0 T λ]
(* MeijerG[{{}, {1., 1.}}, {{0., 0., 4.}, {}}, -1. T λ] *)

• For a simpler form use MeijerG[{{}, {1., 1.}}, {{0., 0., 4.}, {}}, -1. T \[Lambda]] // Rationalize // FunctionExpand // FullSimplify Dec 17, 2015 at 15:08
• Why would you introduce rationalize and Fullsimplify to the expression ? Nov 21, 2020 at 6:11