A "Continuous" Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials

Understand

A novel family of $-1$ orthogonal polynomials called the Chihara polynomials is characterized.

• The polynomials are obtained from a "continuous" limit of the complementary Bannai-Ito polynomials, which are the kernel partners of the Bannai-Ito polynomials.
• The three-term recurrence relation and the explicit expression in terms of Gauss hypergeometric functions are obtained through a limit process.
• A one-parameter family of second-order differential Dunkl operators having these polynomials as eigenfunctions is also exhibited.