Two dimensional Laplace transforms of generalized hypergeometric functions (Q1099365)

The object of the paper is to obtain new operational relations between the original and the image functions that involve Meijer's G-functions. With the help of a known result, the generalized Stieltjes transform of a G-function can be interpreted as a two-dimensional Laplace transform of a function involving the Meijer's G-function, which gives the two main results of the paper. For the possibility of expressing a large number of named special functions by means of the G-symbol, many new operational relations for MacRobert E-functions, Bessel, Legendre, Whittaker and other related generalized hypergeometric functions are duced from the main results by specializing parameters.