Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals

By Francesco Mainardi, Gianni Pagnini. 2003

60 citations recorded by the source corpus.

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.

Subfields: Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/6a3fce1569f5545dc860c9e4c02cf87f06efc0ab

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In Sociology and Political Science

1. Yuri Luchko
2. Virginia S. Kiryakova
3. Francesco Mainardi
4. Gianni Pagnini

Citations in the corpus

• Discrete random walk models for space-time fractional diffusion (2002, unknown): “For a revisited analysis of the pioneering work of Pincherle (Professor of Mathematics at the University of Bologna from 1880 to 1928) we refer to the recent paper by Mainardi and Pagnini [38].”
• Fox H functions in fractional diffusion (2005, unknown): “[23].”
• The mellin integral transform in fractional calculus (2013, methodology): “in [28] (see also [26]) says that the integral in (4.”
• The fundamental solution of the space-time fractional diffusion equation (2007, result): “For a revisited analysis of the pioneering work of Pincherle (18531936, Professor of Mathematics at the University of Bologna from 1880 to 1928) we refer to the recent paper by Mainardi and Pagnini [30].”
• Multi-parametric mittag-leffler functions and their extension (2013, unknown): “Here, we have to mention the brilliant historical and bibliographical description of the early theory of Mellin-Barnes integrals presented in Mainardi and Pagnini [43].”