Some Orthogonal Polynomials Related to Elliptic Functions
نویسندگان
چکیده
منابع مشابه
On Some Orthogonal Functions Generalizing Jack Polynomials
The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group W . Each irreducible representation S of W corresponds to a standard module M(λ) for H. This paper deals with the infinite family G(r, p, n) of complex reflection groups; our goal is to study the standard modules using a commutative subalgebra t of H discovered by Du...
متن کاملConvexity of the zeros of some orthogonal polynomials and related functions
We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between con...
متن کاملOrthogonal Functions Generalizing Jack Polynomials
The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group W and depending on a set of central parameters. Each irreducible representation S of W corresponds to a standard module M(λ) for H. This paper deals with the infinite family G(r, 1, n) of complex reflection groups; our goal is to study the standard modules using a co...
متن کاملOrthogonal polynomials and analytic functions
For a positive definite infinite matrix A, we study the relationship between its associated sequence of orthonormal polynomials and the asymptotic behaviour of the smallest eigenvalue of its truncation An of size n×n. For the particular case of A being a Hankel or a Hankel block matrix, our results lead to a characterization of positive measures with finite index of determinacy and of completel...
متن کاملSeveral Integrability Formulas of Some Functions, Orthogonal Polynomials and Norm Functions
The terminology and notation used here are introduced in the following articles: [10], [21], [17], [6], [20], [1], [9], [13], [2], [4], [18], [15], [5], [8], [11], [14], [12], [16], and [7]. For simplicity, we use the following convention: r, p, x denote real numbers, n denotes an element of N, A denotes a closed-interval subset of R, f , g denote partial functions from R to R, and Z denotes an...
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 Approximation Theory
سال: 2001
ISSN: 0021-9045
DOI: 10.1006/jath.2001.3593