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We investigate several families of multiple orthogonal polynomials associatedwith weights for which the moment generating functions are hypergeometricseries with slightly varying parameters. The weights are supported on the unitinterval, the positive real line, or the unit circle and the multipleorthogonal polynomials are generalizations of the Jacobi, Laguerre or Besselorthogonal polynomials. We give explicit formulas for the type I and type IImultiple orthogonal polynomials and study some of their properties. Inparticular, we describe the asymptotic distribution of the (scaled) zeros ofthe type II multiple orthogonal polynomials via the free convolution. Essentialto our overall approach is the use of the Mellin transform. Finally, we discusstwo applications. First, we show that the multiple orthogonal polynomialsappear naturally in the study of the squared singular values of (mixed)products of truncated unitary random matrices and Ginibre matrices. Secondly,we use the multiple orthogonal polynomials to simultaneously approximatecertain hypergeometric series and to provide an explicit proof of their$\mathbb{Q}$-linear independence.

Applications of multiple orthogonal polynomials with hypergeometric moment generating functions