期刊
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 364, 期 10, 页码 5491-5507出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-2012-05539-5
关键词
Classical orthogonal polynomials; Jacobi polynomials; big q-Jacobi polynomials
类别
We study a new family of classical orthogonal polynomials, here called big - 1 Jacobi polynomials, which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with differential operators of Dunkl type. These polynomials can be obtained from the big q-Jacobi polynomials in the limit q -> -1. An explicit expression of these polynomials in terms of Gauss' hypergeometric functions is found. The big 1 Jacobi polynomials are orthogonal on the union of two symmetric intervals of the real axis. We show that the big - 1 Jacobi polynomials can be obtained from the (terminating) Bannai-Ito polynomials when the orthogonality support is extended to an infinite number of points. We further indicate that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for q -> -1.
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