Article
Licensed
Unlicensed
Requires Authentication
q-Dunkl-classical q-Hermite type polynomials
-
,
Published/Copyright:
May 13, 2014
Abstract.
In this paper, we introduce two symmetric q-Dunkl-classical orthogonal polynomial sets generalizing the Hermite polynomials as range of discrete q-Hermite polynomials I and II by a suitable orthogonality preserving operator. Then, we state some of their properties: explicit expressions, recurrence relations, generating functions, inversion formulas, linear functionals and components. We conclude by locating these polynomials among orthogonal polynomials generalizing Hermite polynomials and classified according to lowering operators.
Keywords: Orthogonal polynomials; symmetric orthogonal polynomials; q-Dunkl operator; generalized Hermite polynomials; discrete q-Hermite polynomials I and II
The authors would like to thank the referee for his/her remarks.
Received: 2012-12-24
Accepted: 2013-5-14
Published Online: 2014-5-13
Published in Print: 2014-6-1
© 2014 by Walter de Gruyter Berlin/Boston
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Frontmatter
- Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
- q-Dunkl-classical q-Hermite type polynomials
- Spectral representation of a Banach-valued stationary random function on a locally compact abelian group
- Sharp weighted norm inequalities for the commutator of Littlewood–Paley operators
- On rearrangement theorems in Banach spaces
- Dynamical contact problems with friction for hemitropic elastic solids
- Multiple solutions for a Dirichlet quasilinear system containing a parameter
- Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1
- A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities
- Transformation of the quasiconformal reflection coefficient and of the Fredholm eigenvalue
- Expansions and asymptotics associated with basic hypergeometric functions and modified q-Bessel functions
Articles in the same Issue
- Frontmatter
- Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
- q-Dunkl-classical q-Hermite type polynomials
- Spectral representation of a Banach-valued stationary random function on a locally compact abelian group
- Sharp weighted norm inequalities for the commutator of Littlewood–Paley operators
- On rearrangement theorems in Banach spaces
- Dynamical contact problems with friction for hemitropic elastic solids
- Multiple solutions for a Dirichlet quasilinear system containing a parameter
- Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1
- A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities
- Transformation of the quasiconformal reflection coefficient and of the Fredholm eigenvalue
- Expansions and asymptotics associated with basic hypergeometric functions and modified q-Bessel functions
