A ‘missing’ family of classical orthogonal polynomials

By Luc Vinet, Alexei S. Zhedanov. 2010

1,242 citations recorded by the source corpus.

We study a family of ‘classical’ orthogonal polynomials which satisfy (apart from a three-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl type. These polynomials can be obtained from the little q-Jacobi polynomials in the limit q = −1. We also show that these polynomials provide a nontrivial realization of the Askey–Wilson algebra for q = −1.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/23d6695e396c94622edd38df143ca12060310914

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

A LIMIT q = −1 FOR THE BIG Q-JACOBI POLYNOMIALS (2012, methodology): “Guided by the q → − 1 limit of the little q -Jacobi polynomials, we derived in [19] an explicit expression of the polynomials P n ( x ) in terms of Gauss’ hypergeometric functions.”
Dunkl shift operators and Bannai-Ito polynomials (2011, background): “6) coincide with the little -1 Jacobi polynomials [32].”
Pruning and Quantization for Deep Neural Network Acceleration: A Survey (2021, methodology): “They found 28.75% test T Liang et al.: Preprint submitted to Elsevier Page 12 of 39 error on CIFAR-10 when setting the threshold to 0.5, if demand a lower error of 15.74% by improving the threshold to 0.99, the inference time will be trebled.”