Premium
Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters
Author(s) -
Durán Antonio J.
Publication year - 2022
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12451
Subject(s) - mathematics , orthogonal polynomials , jacobi polynomials , classical orthogonal polynomials , hahn polynomials , difference polynomials , discrete orthogonal polynomials , wilson polynomials , eigenfunction , differential operator , gegenbauer polynomials , jacobi operator , operator (biology) , sequence (biology) , pure mathematics , bell polynomials , koornwinder polynomials , macdonald polynomials , eigenvalues and eigenvectors , quantum mechanics , physics , biochemistry , chemistry , repressor , genetics , biology , transcription factor , gene
We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second‐order difference or differential operator. In mathematical physics, they allow the explicit computation of bound states of rational extensions of classical quantum‐mechanical potentials. The most apparent difference between classical or classical discrete orthogonal polynomials and their exceptional counterparts is that the exceptional families have gaps in their degrees, in the sense that not all degrees are present in the sequence of polynomials. The new examples have the novelty that they depend on an arbitrary number of continuous parameters.