A "missing" family of classical orthogonal polynomials
Luc Vinet,Alexei Zhedanov +1 more
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In this article, a family of orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type was studied.Abstract:
We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-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 $q=-1$.read more
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The Liver Tumor Segmentation Benchmark (LiTS)
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References
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Supersymmetry and quantum mechanics
TL;DR: In this article, the authors review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications, including shape invariance and operator transformations, and show that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials.
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The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek,René F. Swarttouw +1 more
TL;DR: The Askey-scheme of hypergeometric orthogonal polynomials was introduced in this paper, where the q-analogues of the polynomial classes in the Askey scheme are given.
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Hypergeometric Orthogonal Polynomials and Their q-Analogues
TL;DR: In this paper, Orthogonal Polynomial Solutions of Differential Equations of Real Difference Equations (DDEs) were used to solve Eigenvalue Problems. But they were not used in the context of orthogonal polynomials.