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Multiple orthogonal polynomials satisfy a number of recurrence relations, inparticular there is a $(r+2)$-term recurrence relation connecting the type IImultiple orthogonal polynomials near the diagonal (the so-called step-linerecurrence relation) and there is a system of $r$ recurrence relationsconnecting the nearest neighbors (the so-called nearest neighbor recurrencerelations). In this paper we deal with two problems. First we show how one canobtain the nearest neighbor recurrence coefficients (and in particular therecurrence coefficients of the orthogonal polynomials for each of the definingmeasures) from the step-line recurrence coefficients. Secondly we show how onecan compute the step-line recurrence coefficients from the recurrencecoefficients of the orthogonal polynomials of each of the measures defining themultiple orthogonality.

Computing recurrence coefficients of multiple orthogonal polynomials