The modified Meijer G function is defined by the inverse Laplace transform:

where

and  L is one of three types of integration paths , , and .

Contour  starts at  and finishes at  ().

Contour  starts at  and finishes at  ().

Contour  starts at  and finishes at .

All the paths , , and  put all  poles on the right and all other poles of the integrand (which must be of the form ) on the left.

The classical definition of the Meijer G function is related to the modified definition by

Note: See Prudnikov, Brychkov, and Marichev.

Three noticeable differences between the notations are:

the parameters of the modified Meijer G function are separated out into four natural groups,

 instead of  is placed inside the integral definition of ModifiedMeijerG, and

the pq\mn subscripts and superscripts which are now redundant are omitted.

Use of this function in Maple is not recommended. MeijerG should be used instead.  This function is provided only for backward compatibility.

Prudnikov, A. P.; Brychkov, Yu; and Marichev, O. Integrals and Series, Volume 3: More Special Functions. Gordon and Breach Science, 1990.