منابع مشابه
Matrix-valued little q-Jacobi polynomials
Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2 × 2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and its relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on the m...
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We introduce two kinds of multiple little q-Jacobi polynomials p~n with multi-index ~n = (n1, n2, . . . , nr) and degree |~n| = n1 + n2 + · · · + nr by imposing orthogonality conditions with respect to r discrete little q-Jacobi measures on the exponential lattice {qk, k = 0, 1, 2, 3, . . .}, where 0 < q < 1. We show that these multiple little qJacobi polynomials have useful q-difference proper...
متن کاملUniversal T - matrix , Representations of OSp q ( 1 / 2 ) and Little Q - Jacobi Polynomials
We obtain a closed form expression of the universal T-matrix encapsulating the duality between the quantum superalgebra U q [osp(1/2)] and the corresponding su-pergroup OSp q (1/2). The classical q → 1 limit of this universal T matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp q (1/2) are readily construct...
متن کاملA class of matrix-valued polynomials generalizing Jacobi polynomials
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step recurrence relation, integral inter-relations, and quasi-orthogonality relations. 1. Motivation The understanding of matrix-valued orthogonal polynomi...
متن کاملJu l 2 00 6 Universal T - matrix , Representations of OSp q ( 1 / 2 ) and Little Q - Jacobi Polynomials
We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U q [osp(1/2)] and the corresponding su-pergroup OSp q (1/2). The finite dimensional representations of the quantum su-pergroup OSp q (1/2) are readily constructed employing the said universal T-matrix and the known finite dimensional representations of the dually related deformed ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.10.007