Extension of the Beta function in several variables and applications for multivariate orthogonal polynomials

The fundamental aim of this article is to investigate an extension of the generalized Beta function introduced in (Chaudhry et al. in J. Comput. Appl. Math. 78(1):19–32, 1997) from two variables to three or more variables. The properties of such extended functions are studied in a systematic manner and some inequalities are also discussed. An application for the so-called Laguerre polynomials in n-variables is presented as well.