Simultaneous operational calculus involving a product of a general class of polynomials, Fox's \(H\)-function and the multivariable \(H\)-function
The authors evaluate an integral involving a general polynomial in one variable, a series form of an \(H\)-function of one variable and an \(H\)- function of several variables. The authors call it a bivariate Laplace transform. This integral cannot be called a bivariate Laplace transform. The series form used for the \(H\)-functions is valid only for a particular case of simple poles, which is not mentioned. The bivariate variables \(x\) and \(y\) appear in these functions as a scaling factor in the form \(xy\) and thus the presence of an \(H\)-function of several varibles etc. serves the purpose of the result looking complicated. The result obtained is simply an integral which will be valid under several additional conditions to be stated. Note also that the functions involved are also defined outside the first quadrant.
scientific article; zbMATH DE number 179563