Exceptional Gegenbauer polynomials via isospectral deformation
نویسندگان
چکیده
In this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical polynomials. The construction is based on confluent Darboux transformations, where repeated factorizations at the same eigenvalue are allowed. These allow us Sturm–Liouville problems with polynomial eigenfunctions that have an arbitrary number real-valued parameters. We illustrate new by exhibiting class deformed Gegenbauer polynomials, which XOP families
منابع مشابه
Gegenbauer Polynomials and Semiseparable Matrices
In this paper, we develop a new O(n logn) algorithm for converting coefficients between expansions in different families of Gegenbauer polynomials up to a finite degree n. To this end, we show that the corresponding linear mapping is represented by the eigenvector matrix of an explicitly known diagonal plus upper triangular semiseparable matrix. The method is based on a new efficient algorithm ...
متن کاملInformation entropy of Gegenbauer polynomials
The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in D dimensions. We give an effective method to compute the entropy for Gegenbauer polynomials with an integer parameter and obtain the first few terms in the asymptotic ex...
متن کاملComputing with Expansions in Gegenbauer Polynomials
In this work, we develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. We describe a method to convert a linear combination of Gegenbauer polynomials up to degree n into a representation in a different family of Gegenbauer polynomials with generally O(n log(1/ε)) arithmetic operations where ε is a prescribed accuracy. Special cases where source or targe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2022
ISSN: ['0022-2526', '1467-9590']
DOI: https://doi.org/10.1111/sapm.12510