Multivariable Big and Little q-Jacobi Polynomials
نویسندگان
چکیده
منابع مشابه
UvA - DARE ( Digital Academic Repository ) Multivariable big and little q - Jacobi polynomials
A four-parameter family of multivariable big q-Jacobi polynomials and a threeparameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality is proved with the help of a second-order q-difference operator which is diagonalized by the multivariable polynomials. A link is made between the orthogonality measures and R. Askey’s q-extensions of Sel...
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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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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...
متن کاملNon-classical orthogonality relations for big and little q-Jacobi polynomials
Big q-Jacobi polynomials {Pn(·; a, b, c; q)}∞n=0 are classically defined for 0 < a < q −1, 0 < b < q−1 and c < 0. For the family of little q-Jacobi polynomials {pn(·; a, b|q)}∞n=0, classical considerations restrict the parameters imposing 0 < a < q−1 and b < q−1. In this work we extend both families in such a way that wider sets of parameters are allowed, and we establish orthogonality conditio...
متن کاملStructure relations for the bivariate big q-Jacobi polynomials
The bivariate big q-Jacobi polynomials are defined by [3] Pn,k(x, y; a, b, c, d; q) := Pn−k(y; a, bcq , dq; q) y(dq/y; q)k Pk (x/y; c, b, d/y; q) (n ≥ 0; k = 0, 1, . . . , n), where q ∈ (0, 1), 0 < aq, bq, cq < 1, d < 0, and Pm(t;α, β, γ; q) are univariate big q-Jacobi polynomials, Pm(t;α, β, γ; q) := 3φ2 ( q−m, αβq, t αq, γq ∣∣∣∣ q; q) (m ≥ 0) (see, e.g., [1, Section 7.3]). We give structure r...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 1997
ISSN: 0036-1410,1095-7154
DOI: 10.1137/s0036141095287192