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Selberg-type squared matrices gamma and beta integrals

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2008

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Although Selberg-type, single positive definite symmetric matrices, gamma and beta integrals are evaluated by several authors; see e.g., Askey and Richards (1989), Gupta and Kabe (2005), Mathai (1997), and elsewhere in the vast multivariate statistical analysis literature; the Selberg-type squared matrice gamma and beta interals appear to have been neglected. So also Selberg-type of integrals of positive signature symmetric matrices, skew symmetric matrices are neglected in the literature. This paper records Selberg-type squared matrices beta and gamma integrals.
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  • 3
197-201
  • English

REFERENCES

References: 

1. Askey, Richard and Richards, Donald. Selberg’s second beta integral and an integral of Mehta,
in Probability, Statistics, and Mathematics. Academic Press, New York, (Karlin Volume), (1989).
2. Halberstam, H. and Ingram, R. E. The Mathematical Papers of Sir William Hamilton, Vol. III,
Cambridge University Press, London (1967).
A.Gupta, D. Kabe / Eur. J. Pure Appl. Math, 1 (2008), (197-201) 201
3. Gupta, A. K. and Kabe, D. G. On Selberg’s beta integrals. Random Oper. and Stoch. Eqn. 13,
11-16, 2005.
4. Kabe, D. G. Classical statistical analysis based on a certain hypercomplex multivariate normal
distribution. Metrika 31, 63-76, (1984).
5. Mathai, A. M., Provost, S., and Hayakawa, T. Bilinear Forms and Zonal Polynomials, Springer-
Verlag, New York, (1995).
6. Mathai, A. M. Jacobians of Matrix Transformations. World Scientific, London, (1997).

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