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A remark on the distribution of products of independent normal random variables

Szczepański Jerzy

Science, Technology and Innovation

2020

Vol. 10, no. 3

30--37

We present a proof of the explicit formula of the probability density function of the product of normally distributed independent random variables using the multiplicative convolution formula for Meijer G functions.

Meijer G-functions series as exact solutions of a class of non-homogeneous fractional differential equations

Klimek M., Dziembowski D.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2009

Vol. 8, nr 2

71-85

A fractional differential equation of real order α, containing variable coefficient t β and a non-homogeneous term, is solved. The general solution is obtained as a sum of Meijer G-functions series determining the solution of a homogeneous counterpart of the considered equation and a series representing the particular solution of a non-homogeneous equation. The convergence of the respective series is analyzed in detail using theorems on properties of Meijer G functions. As an example, two equations, with β = 0 and β = α /2 are studied.