Biorthogonal rational functions of 𝑅_{𝐼𝐼}-type

Behera, Kiran; Swaminathan, A.

doi:10.1090/proc/14443

Biorthogonal rational functions of $R_{II}$-type
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by Kiran Kumar Behera and A. Swaminathan

Proc. Amer. Math. Soc. 147 (2019), 3061-3073

DOI: https://doi.org/10.1090/proc/14443

Published electronically: March 15, 2019

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Abstract:

In this work, a sequence of orthonormal rational functions leading to recurrence relations of $R_{II}$-type is constructed. This sequence is proved to be biorthogonal to another sequence of rational functions as well. Two illustrations of such recurrence relations of $R_{II}$-type, one through the associated linear pencil matrix leading to the -1 little Jacobi polynomials and the other through the bilinear transformation yielding the Bannai-Ito polynomials, which are orthogonal on the real line are exhibited.

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