LAUSR

Dual addition formulas: the case of continuous q-ultraspherical and q-Hermite polynomials

Sign Up to like & get
recommendations!
0 Published in 2021 at "Ramanujan Journal"

DOI: 10.1007/s11139-021-00426-7

Abstract: We settle the dual addition formula for continuous q-ultraspherical polynomials as an expansion in terms of special q-Racah polynomials for which the constant term is given by the linearization formula for the continuous q-ultraspherical polynomials.… read more here.

Keywords: hermite polynomials; addition; dual addition; continuous ultraspherical ... See more keywords

Quantum algebra from generalized q-Hermite polynomials

Sign Up to like & get
recommendations!
0 Published in 2017 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2019.07.047

Abstract: Abstract In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomials h ˜ n , α ( x ; q ) , introduced by Mezlini et al. in 2014. Our… read more here.

Keywords: quantum algebra; algebra generalized; hermite polynomials; generalized hermite ... See more keywords

Generating functions for generalized Hermite polynomials associated with parabolic cylinder functions

Sign Up to like & get
recommendations!
0 Published in 2019 at "Integral Transforms and Special Functions"

DOI: 10.1080/10652469.2019.1697695

Abstract: ABSTRACT In this article, we first give some basic properties of generalized Hermite polynomials associated with parabolic cylinder functions. We next use Weisnerś group theoretic method and operational rules method to establish new generating functions… read more here.

Keywords: generalized hermite; associated parabolic; generating functions; hermite polynomials ... See more keywords

Roots of generalised Hermite polynomials when both parameters are large

Sign Up to like & get
recommendations!
0 Published in 2019 at "Nonlinearity"

DOI: 10.1088/1361-6544/abdd93

Abstract: We study the roots of the generalised Hermite polynomials H m,n when both m and n are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called the elliptic… read more here.

Keywords: generalised hermite; parameters large; hermite polynomials; roots generalised ... See more keywords

Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials

Sign Up to like & get
recommendations!
0 Published in 2018 at "International Mathematics Research Notices"

DOI: 10.1093/imrn/rny172

Abstract: The Painlevé-IV equation has three families of rational solutions generated by the generalized Hermite polynomials. Each family is indexed by two positive integers $m$ and $n$. These functions have applications to nonlinear wave equations, random… read more here.

Keywords: rational painlev; generalized hermite; functions associated; hermite polynomials ... See more keywords

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

Sign Up to like & get
recommendations!
0 Published in 2019 at "International Journal of Geometric Methods in Modern Physics"

DOI: 10.1142/s0219887820500218

Abstract: We use the recursion relations of the continuous q-Hermite polynomials and obtain the q-difference realizations of the ladder operators of a q-oscillator algebra in terms of the Askey–Wilson operat... read more here.

Keywords: oscillator algebra; approach continuous; hermite polynomials; continuous hermite ... See more keywords

On the complex Hermite polynomials

Sign Up to like & get
recommendations!
1 Published in 2020 at "Filomat"

DOI: 10.2298/fil2002409l

Abstract: In this paper we use a set of partial differential equations to prove an expansion theorem for multiple complex Hermite polynomials. This expansion theorem allows us to develop a systematic and completely new approach to… read more here.

Keywords: expansion; complex hermite; hermite polynomials;

On Spectral Vectorial Differential Equation of Generalized Hermite Polynomials

Sign Up to like & get
recommendations!
0 Published in 2022 at "Axioms"

DOI: 10.3390/axioms11070344

Abstract: In this paper, we first give some results on monic generalized Hermite polynomials (GHP) {Hn(μ)(x)}n≥0, orthogonal with respect to the positive weight |x|2μe−x2,μ>−12,x∈R, which will lead to the formulation of the second-order spectralvectorial differential equation… read more here.

Keywords: equation; spectral vectorial; differential equation; hermite polynomials ... See more keywords

Coefficient Estimates of New Families of Analytic Functions Associated with q-Hermite Polynomials

Sign Up to like & get
recommendations!
0 Published in 2023 at "Axioms"

DOI: 10.3390/axioms12010052

Abstract: In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, we establish the bounds of the initial coefficients υ2, υ3, and υ4 of the Taylor–Maclaurin series and that of… read more here.

Keywords: coefficient estimates; analytic functions; estimates new; new families ... See more keywords

Some Identities Involving Degenerate q-Hermite Polynomials Arising from Differential Equations and Distribution of Their Zeros

Sign Up to like & get
recommendations!
1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14040706

Abstract: This paper intends to define degenerate q-Hermite polynomials, namely degenerate q-Hermite polynomials by means of generating function. Some significant properties of degenerate q-Hermite polynomials such as recurrence relations, explicit identities and differential equations are established.… read more here.

Keywords: differential equations; zeros; degenerate hermite; hermite polynomials ... See more keywords