A VARIANT OF THE TYPE-1 BETA AND DIRICHLET INTEGRALS
Journal Title: Journal of Ramanujan Society of Mathematics and Mathematical Sciences - Year 2017, Vol 6, Issue 1
Abstract
A double integral, which can be taken as an extension of a type-1 beta integral, is introduced and its properties are studied. Than a $k$-variate multiple integral on a unit cube in Euclidean $k$-space is introduced, which will produce the total integral equivalent to the total integral in a $(k-1)$-variate type-1 Dirichlet integral, or the integral over a simplex in a $(k-1)$-flat. Several properties of this multiple integral are studied. Marginal functions and Mellin transform are examined. Several transformations are given, finally leading to a type-1 Dirichlet integral. Statistical densities connected with the integrand of the extended Dirichlet integral are also discussed.
Authors and Affiliations
A. M. Mathai
Keywords
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