Recurrence Asymptotics in a Family of Matrix Semi-Classical Laguerre Polynomials

In this paper, we present a new three-parameter semi-classical Laguerre matrix weight function and explore the associated sequence of matrix orthogonal polynomials. We derive explicit expressions for the corresponding three-term recurrence relations, both in terms of their scalar counterparts and scalar Hankel determinants. Finally, we analyze the asymptotic behavior of the recurrence coefficients with respect to the variables t and n.