Differential properties of Meijer's G-function

The kth derivative of any Meijer G-function whose argument is proportional to any rational power of the variable is obtained in terms of another G-function. Many known formulae for derivatives of G-functions are easily derived from our result. The authors also obtain, in passing, both an apparently new relationship for rearranging parameters of a special G-function, and the Fourier sine transform of a G-function whose argument is a rational power of the variable. Applications are made to several examples of physical and mathematical interest, such as the Holtsmark function used in stellar dynamics and plasma spectroscopy.