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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 564287, 8 pages
http://dx.doi.org/10.1155/2015/564287
Research Article

Infinite Matrix Products and the Representation of the Matrix Gamma Function

1Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
2CIMAT, 36000 Guanajuato, GTO, Mexico
3Universidad Autónoma de Aguascalientes, 20131 Aguascalientes, AGS, Mexico

Received 24 October 2015; Accepted 25 November 2015

Academic Editor: Allan Peterson

Copyright © 2015 J.-C. Cortés et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.