Results 51 to 60 of about 147 (140)

On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2006
The dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(mu (x;s)|q)$ correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations.
Valentyna A. Groza, Ivan I. Kachuryk
doaj  

A model for the continuous q-ultraspherical polynomials [PDF]

Journal of Mathematical Physics, 1995
An algebraic interpretation for two classes of continuous q-polynomials is provided. Rogers’ continuous q-Hermite polynomials and continuous q-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the q-Heisenberg algebra and a q-deformation of the Euclidean algebra in these dimensions.
Floreanini, Roberto, Vinet, Luc
openaire   +3 more sources

Asymptotic Properties of Derivatives of the Stieltjes Polynomials

Journal of Applied Mathematics, 2012
Let 𝑤𝜆(𝑥)∶=(1−𝑥2)𝜆−1/2 and 𝑃𝜆,𝑛(𝑥) be the ultraspherical polynomials with respect to 𝑤𝜆(𝑥). Then, we denote the Stieltjes polynomials with respect to 𝑤𝜆(𝑥) by 𝐸𝜆,𝑛+1(𝑥) satisfying ∫1−1𝑤𝜆(𝑥)𝑃𝜆,𝑛(𝑥)𝐸𝜆,𝑛+1(𝑥)𝑥𝑚𝑑𝑥=0, 0 ...
Hee Sun Jung, Ryozi Sakai
doaj   +1 more source

ONE-SIDED \(L\)-APPROXIMATION ON A SPHERE OF THE CHARACTERISTIC FUNCTION OF A LAYER

Ural Mathematical Journal, 2018
In the space \(L(\mathbb{S}^{m-1})\) of functions integrable on the unit sphere \(\mathbb{S}^{m-1}\) of the Euclidean space \(\mathbb{R}^{m}\) of dimension \(m\ge 3\), we discuss the problem of one-sided approximation to the characteristic function of a ...
Marina V. Deikalova, Anastasiya Yu. Torgashova   +1 more
doaj   +1 more source

ON INTERPOLATION POLYNOMIALS USING THE ROOTS OF ULTRASPHERICAL POLYNOMIALS

Demonstratio Mathematica, 1984
Denote by \(x_ n,x_{n-1},...,x_ 1\) the roots of the ultraspherical polynomial \[ P_ n^{\alpha}(x)=(-1)^ n/(2^ nn!)(1-x^ 2)^{- \alpha}\frac{d^ n}{dx^ n}(1-x^ 2)^{n+\alpha}, \] where \(\alpha >- 1\) \((n=1,2,...)\) and consider the partition of [-1,1], \(\Delta ...
openaire   +2 more sources

The product of two ultraspherical polynomials [PDF]

Proceedings of the Glasgow Mathematical Association, 1961
LetIt is familiar that(1) In the addition theorem [3, p. 363]wheretake θ = π and replace v by v−½.
openaire   +1 more source

Integral Representations of Ultraspherical Polynomials II

, 2021
The results in this paper replace Section 4 in arXiv:1812 ...
Bingham, N. H., Symons, Tasmin L.
openaire   +2 more sources

Representations of the Quantum Algebra su_q(1,1) and Discrete q-Ultraspherical Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2005
We derive orthogonality relations for discrete q-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly.
Valentyna Groza
doaj  

Nonnegative linearization of the associated $g$-ultraspherical polynomials [PDF]

Methods and Applications of Analysis, 1995
Nonnegative product linearization of the associated continuous \(q\)-ultraspherical polynomials is shown for all values \(-1 ...
openaire   +1 more source

Spectral Analysis of Certain Schrödinger Operators

Symmetry, Integrability and Geometry: Methods and Applications, 2012
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators.
Mourad E.H. Ismail, Erik Koelink
doaj   +1 more source