A survey on D-semiclassical orthogonal polynomials.
A symbolic operator approach to power series transformation-expansion formulas.
A transplantation theorem for ultraspherical polynomials at critical index
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with .
A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions
2000 Mathematics Subject Classification: 33A65, 33C20.A unifed group-theoretic method of obtaining more general class of generating functions from a given class of improper partial semi-bilateral generating functions involving Laguerre and Gegenbauer polynomials are discussed.
Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme.
Affine transformations of a Leonard pair.
Algebraic properties of a family of Jacobi polynomials
The one-parameter family of polynomials is a subfamily of the two-parameter family of Jacobi polynomials. We prove that for each , the polynomial is irreducible over for all but finitely many . If is odd, then with the exception of a finite set of , the Galois group of is ; if is even, then the exceptional set is thin.
Algorithm 47. Solution of a first-order non-linear differential equation in Chebyshev series
Alternative orthogonal polynomials and quadratures.
An alternative definition of the Hermite polynomials related to the Dunkl Laplacian.
An analogue of a problem of J. Balázs and P. Turán, II (Inequalities)
An Application for the Chebyshev Polynomials
An application of hypergeometric functions to a problem in function theory.
An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials.
An exactly solvable spin chain related to Hahn polynomials.
An example of nonsymmetric semi-classical form of class ; generalization of a case of Jacobi sequence.
An expansion formula for the H-function involving generalized Legendre associated functions
An extension of typically-real functions and associated orthogonal polynomials
Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties...
An inequality for Chebyshev connection coefficients.
An integral operator inequality with applications.