Hahn multiple orthogonal polynomials of type I: Hypergeometric expressions

Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kamp e de Feriet hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Then, part of the Askey scheme for multiple orthogonal polynomials type I is completed. In particular, explicit expressions in terms of generalized hypergeometric series and Kamp e de Feriet hypergeometric series, are given for the multiple orthogonal polynomials of type I for the Jacobi-Pineiro, Meixner I, Meixner II, Kravchuk, Laguerre I, Laguerre II and Charlier families.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).