<b><i>q</i></b>-Laguerre and Wall polynomials are related by the Fourier - Gauss transform

Atakishiyeva, M. K.; Atakishiyev, Natig M.

doi:10.1088/0305-4470/30/13/001

Cited by 10 publications

(7 citation statements)

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“…Our results for a significantly wide class of q-polynomials are potentially useful in some of these fields. With a view to motivating the interested readers toward the theory and widespread applications of various families of q-series, q-polynomials, as well as q-difference and q-derivative operators, we have chosen here to include references (see, for example, [33][34][35][36][37][38][39][40][41][42][43][44][45]) to various related developments in recent years.…”

Section: Further Remarks and Observationsmentioning

confidence: 99%

Generalized q-Difference Equations for q-Hypergeometric Polynomials with Double q-Binomial Coefficients

2022

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In this paper, we apply a general family of basic (or q-) polynomials with double q-binomial coefficients as well as some homogeneous q-operators in order to construct several q-difference equations involving seven variables. We derive the Rogers type and the extended Rogers type formulas as well as the Srivastava-Agarwal-type bilinear generating functions for the general q-polynomials, which generalize the generating functions for the Cigler polynomials. We also derive a class of mixed generating functions by means of the aforementioned q-difference equations. The various results, which we have derived in this paper, are new and sufficiently general in character. Moreover, the generating functions presented here are potentially applicable not only in the study of the general q-polynomials, which they have generated, but indeed also in finding solutions of the associated q-difference equations. Finally, we remark that it will be a rather trivial and inconsequential exercise to produce the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional forced-in parameter p is obviously redundant.

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Section: Further Remarks and Observationsmentioning

confidence: 99%

Generalized q-Difference Equations for q-Hypergeometric Polynomials with Double q-Binomial Coefficients

2022

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“…(3.21.1)]. They appear in several branches of mathematics and physics, and their generalization arise in many applications (see for details, [2,4,3,13,14,21]), such as (for example) quantum group, q-harmonic oscillator and coding theory, and so on.…”

Section: Introductionmentioning

confidence: 99%

Certain generating functions for Cigler's polynomials

Arjika

2021

Preprint

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“…Letting r = a = 0, c k = (−1) k (α; q) k (η; q) k /(γ; q) k and y = 1 in 7gives (5). Choosing r = −1, a = 0, c k = (α; q) k (η; q) k /(γ; q) k and y = 1 in (7) yields (6).…”

Section: Introductionmentioning

confidence: 99%

Generalized q-Laguerre type polynomials and q-partial differential equations

Niu

2019

Filomat

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In this paper we define the q-Laguerre type polynomials U n (x, y, z; q), which include q-Laguerre polynomials, generalized Stieltjes-Wigert polynomials, little q-Laguerre polynomials and q-Hermite polynomials as special cases. We also establish a generalized q-differential operator, with which we build the relations between analytic functions and U n (x, y, z; q) by using certain q-partial differential equations. Therefore, the corresponding conclusions about q-Laguerre polynomials, little q-Laguerre polynomials and q-Hermite polynomials are gained as corollaries. As applications, some generating functions and generalized Andrews-Askey integral formulas are given in the final section.

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q-Laguerre and Wall polynomials are related by the Fourier - Gauss transform

Cited by 10 publications

References 10 publications

Generalized q-Difference Equations for q-Hypergeometric Polynomials with Double q-Binomial Coefficients

Generalized q-Difference Equations for q-Hypergeometric Polynomials with Double q-Binomial Coefficients

Certain generating functions for Cigler's polynomials

Generalized q-Laguerre type polynomials and q-partial differential equations

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