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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A class of integral identities with Hermitian matrix argument


Authors: Daya K. Nagar, Arjun K. Gupta and Luz Estela Sánchez
Journal: Proc. Amer. Math. Soc. 134 (2006), 3329-3341
MSC (2000): Primary 33E99; Secondary 62H99
Published electronically: May 12, 2006
MathSciNet review: 2231918
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Abstract: The gamma, beta and Dirichlet functions have been generalized in several ways by Ingham, Siegel, Bellman and Olkin. These authors defined them as integrals having the integrand as a scalar function of real symmetric matrix. In this article, we have defined and studied these functions when the integrand is a scalar function of Hermitian matrix.


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Additional Information

Daya K. Nagar
Affiliation: Departamento de Matemáticas, Universidad de Antioquia, Medellín, AA 1226, Colombia
Email: nagar@matematicas.udea.edu.co

Arjun K. Gupta
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403-0221
Email: gupta@bgnet.bgsu.edu

Luz Estela Sánchez
Affiliation: Departamento de Matemáticas, Universidad de Antioquia, Medellín, AA 1226, Colombia
Email: lesanchez@matematicas.udea.edu.co

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08602-3
PII: S 0002-9939(06)08602-3
Keywords: Beta function, Dirichlet function, gamma function, Liouville integral, matrix variate, transformation
Received by editor(s): June 10, 2003
Received by editor(s) in revised form: November 5, 2004, and June 1, 2005
Published electronically: May 12, 2006
Additional Notes: The first and third authors were supported by the Comité para el Desarrollo de la Investigación, Universidad de Antioquia research grant no.\ IN387CE
Communicated by: Richard A. Davis
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.