On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
نویسندگان
چکیده
منابع مشابه
Two-variable orthogonal polynomials of big q-Jacobi type
A four-parameter family of orthogonal polynomials in two variables is defined by 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 ∈ N; 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]...
متن کاملMatrix-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...
متن کامل4 Multiple little q - Jacobi polynomials ⋆
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 کاملOn the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from q-Racah to Racah polynomials ar...
متن کاملQ-Hermite Polynomials and Classical Orthogonal Polynomials
We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.02.034