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On Selberg's beta integrals
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A. K. Gupta
Published/Copyright:
January 1, 2005
Askey and Richards (1989) evaluate Selberg's first and second beta integrals using Aomoto's (1987) formidable methodology of setting and solving a first order difference equation. Using this methodology they evaluate certain other beta and gamma type integrals. However, Selberg's first and second beta and gamma type integrals very elegantly fit within the framework of hypercomplex multivariate normal distribution theory developed by Kabe (1984), and hence can be evaluated using the known multivariate normal distribution theory integrals.
Key Words: Selberg's first beta integral;; hypercomplex normal multivariate distribution theory;; Wishart density;; multivariate beta density;; roots density; Stirling's integral.
Published Online: 2005-01-01
Published in Print: 2005-01-01
Copyright 2005, Walter de Gruyter
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Articles in the same Issue
- The stochastic maximum principle in optimal control of singular diffusions with non linear coefficients
- On Selberg's beta integrals
- Subordination of symmetric quasi -regular Dirichlet forms
- A note on the asymptotic behavior of sequences of generalized subgaussian random vectors
- The Circular Law. Twenty years later. Part III
- Corrigendum
Articles in the same Issue
- The stochastic maximum principle in optimal control of singular diffusions with non linear coefficients
- On Selberg's beta integrals
- Subordination of symmetric quasi -regular Dirichlet forms
- A note on the asymptotic behavior of sequences of generalized subgaussian random vectors
- The Circular Law. Twenty years later. Part III
- Corrigendum
