  This paper addresses two primary objectives in the realm of classical
multiple orthogonal polynomials with an arbitrary number of weights. Firstly,
it establishes new and explicit hypergeometric expressions for type I Hahn
multiple orthogonal polynomials. Secondly, applying the residue theorem and the
Mellin transform, the paper derives contour integral representations for
several families of orthogonal polynomials. Specifically, it presents contour
integral formulas for both type I and type II multiple orthogonal polynomials
in the Laguerre of the first kind, Jacobi-Pi\~neiro, and Hahn families. The
evaluation of these integrals leads to explicit hypergeometric representations.
