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arXiv · 1712.00567

Biorthogonal rational functions of $R_{II}$ type

Kiran Kumar Behera·A. Swaminathan
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Abstract

In this work, a sequence of orthonormal rational functions that is also biorthogonal to another sequence of rational functions arising from recurrence relations of $R_{II}$ type is constructed. The biorthogonality is proved by a procedure which we call Zhedanov method. A particular case of a sequence of orthonormal rational functions having denominators of special form is considered to motivate the general case. The particular case provides a Christoffel type transformation of the generalized eigenvalue problem with a reformulation different from the existing literature.

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Kiran Kumar Behera, A. Swaminathan. 2017-12-02. Biorthogonal rational functions of $R_{II}$ type. https://doi.org/10.1090/proc/14443

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