Generating function for the Bannai-Ito polynomials

Bergeron, Geoffroy; Vinet, Luc; Tsujimoto, Satoshi

doi:10.1090/proc/14158

Generating function for the Bannai-Ito polynomials
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by Geoffroy Bergeron, Luc Vinet and Satoshi Tsujimoto

Proc. Amer. Math. Soc. 146 (2018), 5077-5090

DOI: https://doi.org/10.1090/proc/14158

Published electronically: September 10, 2018

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Abstract:

A generating function for the Bannai-Ito polynomials is derived using the fact that these polynomials are known to be essentially the Racah or $6j$ coefficients of the $\mathfrak {osp}(1|2)$ Lie superalgebra. The derivation is carried in a realization of the recoupling problem in terms of three Dunkl oscillators.

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