On sieved orthogonal polynomials. VIII. Sieved associated Pollaczek polynomials
نویسندگان
چکیده
منابع مشابه
On a Pollaczek-Jacobi type orthogonal polynomials
We study a sequence of polynomials orthogonal with respect to a family weights w(x) := w(x, t) = e x(1− x) , t ≥ 0, over [−1, 1]. If t = 0, this reduces to a shifted Jacobi weight. Our ladder operator formalism and the associated compatibility conditions give an easy determination of the recurrence coefficients. For t > 0, the deformation term e−t/x induces an infinitely strong zero at x = 0. T...
متن کاملCharacterizations of Generalized Hermite and Sieved Ultraspherical Polynomials
A new characterization of the generalized Hermite polynomials and of the orthogonal polynomials with respect to the measure |x|γ(1 − x2)1/2dx is derived which is based on a “reversing property” of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalizati...
متن کاملPainlevé V and a Pollaczek-Jacobi type orthogonal polynomials
We study a sequence of polynomials orthogonal with respect to a one parameter family of weights w(x) := w(x, t) = e x(1− x) , t ≥ 0, defined for x ∈ [0, 1]. If t = 0, this reduces to a shifted Jacobi weight. Our ladder operator formalism and the associated compatibility conditions give an easy determination of the recurrence coefficients. For t > 0, the factor e−t/x induces an infinitely strong...
متن کاملSymmetric Orthogonal Polynomials and the Associated Orthogonal L-polynomials
We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.
متن کاملShannon entropy of symmetric Pollaczek polynomials
We discuss the asymptotic behavior (as n → ∞) of the entropic integrals En = − ∫ 1 −1 log ( p n (x) ) p n (x)w(x) dx , and Fn = − ∫ 1 −1 log ( p n (x)w(x) ) p n (x)w(x) dx, when w is the symmetric Pollaczek weight on [−1, 1] with main parameter λ ≥ 1, and pn is the corresponding orthonormal polynomial of degree n. It is well known that w does not belong to the Szegő class, which implies in part...
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: 1992
ISSN: 0021-9045
DOI: 10.1016/0021-9045(92)90107-y