Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals

Details Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals

2007-02-18

arxiv.org/abs/math/0702520v1

Journal of Computational and Applied Mathematics, Vol. 153 (2003), pp. 331-342

Mathematics

Complex Variables

17 pages

Scientific paper

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.

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