Multiple orthogonal polynomials with respect to Gauss' hypergeometric function

A new set of multiple orthogonal polynomials both type I and II with respect to two weight functions involving Gauss' hypergeometric function on the interval (0,1) is studied. This has direct applications in investigation singular values products Ginibre random matrices are connected branched continued fractions total-positivity problems combinatorics. The pair orthogonality measures shown be a Nikishin system satisfy matrix Pearson-type differential equation. focus whose indices lie step-line, for which it that differentiation gives shift parameters, therefore satisfying Hahn's property. We obtain Rodrigues-type formulas functions, while more detailed characterization given (aka 2-orthogonal polynomials) include an explicit expression as terminating series, third-order equation, recurrence relation. asymptotic behavior their coefficients mimics those Jacobi–Piñeiro polynomials, based zero distribution Mehler–Heine formula near origin given. Particular choices parameters confluence relations give some known systems such special cases Jacobi-type components cubic decomposition threefold symmetric Hahn-classical confluent second kind.