Reproducing kernels for $q$-Jacobi polynomials
نویسندگان
چکیده
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...
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The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel relating little q-Jacobi function transforms for different parameter sets. A product formula for the dual transmutation kernel is obtained. For the inverse transform the transmutation kernel is given as a 3φ2-series, ...
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We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0454104-5