Some Clebsch-Gordan type linearization relations and associated families of Dirichlet integrals

Motivated essentially by some potentially useful Clebsch-Gordan type linearization relations for the Laguerre polynomials, the authors evaluate certain families of multiple Dirichlet integrals involving the products of several Laguerre polynomials. Relevant connections of the main results presented here with various known integral formulas are also considered.