2024/02/09 by Luo, Yu, Tsujimoto, Satoshi, Yang, Hao
#33C45 #33C47 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.06197
Exceptional extensions of a class of Laurent biorthogonal polynomials (the so-called Hendriksen-van Rossum polynomials) have been presented by the authors recently. This is achieved through Darboux transformations of generalized eigenvalue problems. In this paper, we discuss the recurrence relations satisfied by these exceptional Laurent biorthogonal polynomials and provide a type of recurrence relations with 3l0+4 terms explicitly, where the parameter l0 corresponds to the degree of the polynomial part in the seed function used in the Darboux transformation. In the proof of these recurrence relations, the backward operator which maps an exceptional polynomial into a classical one plays a significant role.