PreprintCC BY 4.0arXiv
Continuous representations of the meta Hahn algebra and special functions
Abstract
Infinite families of biorthogonal rational functions are constructed using infinite dimensional representations of the three-generated meta Hahn algebra. Continuous Hahn and continuous dual Hahn polynomials are also recovered along the way using an embedding of the Hahn algebra inside the meta Hahn. Rational functions and polynomials arise as transition coefficients between eigenvectors and generalized eigenvectors, and their algebraic properties follow naturally from the relations of the meta Hahn algebra. Finally, biorthogonality relations are established for the rational functions introduced in the paper.
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BibTeX
@misc{labriet2026continuous,
title = {{Continuous representations of the meta Hahn algebra and special functions}},
author = {Quentin Labriet and Luc Vinet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21494},
eprint = {2610.21494},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21494},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuous representations of the meta Hahn algebra and special functions
AU - Quentin Labriet
AU - Luc Vinet
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21494
UR - https://arxiv.org/abs/2610.21494
AB - Infinite families of biorthogonal rational functions are constructed using infinite dimensional representations of the three-generated meta Hahn algebra. Continuous Hahn and continuous dual Hahn polynomials are also recovered along the way using an embedding of the Hahn algebra inside the meta Hahn. Rational functions and polynomials arise as transition coefficients between eigenvectors and generalized eigenvectors, and their algebraic properties follow naturally from the relations of the meta Hahn algebra. Finally, biorthogonality relations are established for the rational functions introduced in the paper.
ER -