Piñeiro mixed orthogonal polynomials and bidiagonal factorization

We study mixed multiple orthogonal polynomials associated with rank-one matrices of measures and their recurrence relations. On the step line we identify the corresponding banded recurrence matrix through the Gauss–Borel factorization of the moment matrix. Elementary Christoffel transformations lead to a factorization of this recurrence matrix into lower and upper bidiagonal factors. For the mixed Piñeiro system we derive contour-integral and generalized hypergeometric representations and formulas for the recurrence and factorization coefficients.