Darboux-type formula for Jacobi biorthogonal polynomials
Zhaofeng Lin, Kai Wang, Zhanhang Zheng
TL;DR
This paper derives a Darboux-type asymptotic formula for Jacobi biorthogonal polynomials using steepest descent, extending classical results to the biorthogonal setting.
Contribution
It introduces a Darboux-type asymptotic formula for Jacobi biorthogonal polynomials, generalizing classical orthogonal polynomial results.
Findings
Established a Darboux-type formula for Jacobi biorthogonal polynomials
Constructed a suitable contour for steepest descent analysis
Reduced to classical Darboux formula in the orthogonal case
Abstract
In this paper, we study the asymptotic behavior of Jacobi biorthogonal polynomials. A Darboux-type formula is established using the method of steepest descent. In the proof, we construct an appropriate contour to apply the Rodrigues formula. Our result reduces to the classical Darboux formula in the orthogonal case.
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