Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals

Authors:
Francesco Mainardi;Gianni Pagnini
Affiliations:
Dipartimento di Fisica, Università di Bologna and INFN, Sezione di Bologna, Via Irnerio 46, I-40126 Bologna, Italy;Istituto per le Scienze dell'Atmosfera e del Clima del CNR, Via Gobetti 101, I-40129 Bologna, Italy
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

Citing 1
Cited 3

An introduction to difference equations

An introduction to difference equations

Fox H functions in fractional diffusion

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order

Journal of Computational and Applied Mathematics
Fox H functions in fractional diffusion

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The 1888 paper by Salvatore Pincherle (Professor of Mathematics at the University of Bologna) on generalized hypergeometric functions is revisited. We point out the pioneering contribution of the Italian mathematician towards the Mellin-Barnes integrals based on the duality principle between linear differential equations and linear difference equation with rational coefficients. By extending the original arguments used by Pincherle, we also show how to formally derive the linear differential equation and the Mellin-Barnes integral representation of the Meijer G functions.