Hankel Determinants from Quadratic Orthogonal Pairs for Hyperelliptic Functions and Their Applications

This paper introduces a novel method for constructing Hankel determinants using quadratic orthogonal pairs in the context of hyperelliptic functions. The authors explore the theoretical foundations and present various applications, demonstrating the utility of this approach in solving complex problems in integrable systems and related areas. This research has significant potential for applications in various fields of mathematics and theoretical physics, particularly in the study of integrable systems and special functions.