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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
Posted:
May 12, 2006
MathSciNet review:
2231918
Full-text PDF Free Access
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Additional Information
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.
References
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A. K. Gupta and D. K. Nagar, Matrix Variate Distributions, Chapman & Hall/CRC, Boca Raton, 2000. MR 1738933 (2001d:62055)
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A. E. Ingham, An integral which occurs in statistics, Proc. Cambridge Philos. Soc., 29 (1933), 271-276.
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I. Olkin, A class of integral identities with matrix argument, Duke Math. J., 26 (1959), 207-213. MR 0101223 (21:36)
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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
Posted:
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 after
28 years from publication.
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