Multiple orthogonal polynomials, irrationality and transcendence

We explain the notion of multiple orthogonal polynomials (polyorthogonal polynomials), which is closely related to Hermite-Padé rational approximation of a system of Markov functions, and give some explicit examples. As an application we show how multiple orthogonal polynomials can be used to give a constructive proof of irrationality of certain real numbers and also of transcendence of real numbers. Historically Hermite-Padé approximation was introduced by Hermite to prove the transcendence of e.status: publishe