منابع مشابه
Uniform multi - parameter limit transitions in the Askey tableau
1. Elementary limit formulas We consider the classical orthogonal polynomials as monic polynomials pn(x) = x + terms of degree less than n. We have • Jacobi polynomials p (α,β) n (x) with respect to weight function (1 − x) (1 + x) on (−1, 1); • Laguerre polynomials ln(x) with respect to weight function e −x x on (0,∞); • Hermite polynomials hn(x) with respect to weight function e −x on (−∞,∞). ...
متن کاملThe Associated Askey-wilson Polynomials
We derive some contiguous relations for very well-poised 8<^7 series and use them to construct two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials. We then use these solutions to find explicit representations of two families of associated Askey-Wilson polynomials. We identify the corresponding continued fractions as quotients of tw...
متن کاملThe Universal Askey–Wilson Algebra
Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. We define an associative F-algebra ∆ = ∆q by generators and relations in the following way. The generators are A, B, C. The relations assert that each of A+ qBC − q−1CB q2 − q−2 , B + qCA− q−1AC q2 − q−2 , C + qAB − q−1BA q2 − q−2 is central in ∆. We call ∆ the universal Askey–Wilson algebra. We discuss how ∆ is related to the orig...
متن کاملExpansions in the Askey–Wilson Polynomials
We give a general expansion formula of functions in the Askey–Wilson polynomials and using the Askey–Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey–Wilson type, which are not necessarily orthogonal. Limiting cases give expansions in little and big q-Jacobi type polynomials. We also give a new generating funct...
متن کاملWeinstein's Functions and the Askey-gasper Identity Weinstein's Functions and the Askey-gasper Identity
In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was found by Askey and Gasper in 1973, published in 1976. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realize...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00167-8