Ratio asymptotics for multiple orthogonal polynomials
Walter Van Assche

TL;DR
This paper investigates the asymptotic behavior of ratios of neighboring multiple orthogonal polynomials, assuming the convergence of recurrence coefficients, providing insights into their long-term behavior.
Contribution
It establishes the ratio asymptotics for multiple orthogonal polynomials under recurrence coefficient convergence, advancing understanding in this area.
Findings
Derived asymptotic formulas for polynomial ratios
Connected recurrence coefficient convergence to polynomial behavior
Enhanced theoretical understanding of multiple orthogonal polynomials
Abstract
We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the recurrence coefficients in the nearest neighbor recurrence relations converge.
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