The q-exponential operator

Saad, Husam L.; Sukhi, Abbas A.

doi:10.12988/ams.2013.24287

Cited by 7 publications

(6 citation statements)

References 21 publications

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“…(1.13) (4) Upon setting (α, r, s, y, a) = (∞, −1, 0, 1, −q), the generalized q-polynomials L(r,s) n (α, x, y, z, a) reduce to the homogeneous Rogers-Szegö polynomials h n (x, y|q) (see [18]):…”

Section: Remarkmentioning

confidence: 99%

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

Cao¹,

Hounkonnou²

2021

Preprint

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In this paper, we use the generalized q-polynomials with double q-binomial coefficients and homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837-851.] to construct q-difference equations with seven variables, which generalize recent works of Jia et al [Symmetry 2021[Symmetry , 13, 1222. In addition, we derive Rogers formulas, extended Rogers formulas and Srivastava-Agarwal type bilinear generating functions for generalized qpolynomials, which generalize generating functions for Cigler's polynomials [J. Difference Equ. Appl. 24 (2018), 479-502.]. Finally, we also derive mixed generating functions using q-difference equations.

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Section: Remarkmentioning

confidence: 99%

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

Cao¹,

Hounkonnou²

2021

Preprint

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“…Suppose that the operator R(y D q ) acts upon the variable x. We then have the following consequence (see [15] and [17]):…”

Section: Introductionmentioning

confidence: 99%

Some homogeneous q-difference operators and the associated generalized Hahn polynomials

Srivástava¹,

Kelil²

2019

Appl. Set-Valued Anal. Optim.

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In this paper, we first construct the homogeneous q-shift operator E(a, b; D q) and the homogeneous q-difference operator L(a, b; Θ x,y). We then apply these operators in order to represent and investigate a family of generalized Cauchy polynomials and a general form of the q-Hahn polynomials. We derive some q-identities such as generating functions, extended generating functions, Mehler's formula and Rogers' formula for these q-polynomials. Relevant connections of the q-identities presented here with a number of known or new results associated with various specialized families of q-polynomials are also considered.

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“…Recently, Saad and Sukhi [13] have introduced the following q-exponential operator R(bD q ) as follows…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by Saad and Sukhi [13], Srivastava and Abdlhusein [15] works, our interest is to introduce new homogeneous q-difference operators E(a, b; D q ) and T (a, b; θ xy ). The first homogeneous q-difference operator E(a, b; D q ) is defined by…”

Section: Introductionmentioning

confidence: 99%

Some homogeneous $q$-difference operators and the associated generalized Hahn polynomials

Srivastava,

Arjika,

Kelil

2019

Preprint

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In this paper, we first construct the homogeneous q-shift operator E(a, b; D q ) and the homogeneous q-difference operator L(a, b; θ xy ). We then apply these operators in order to represent and investigate generalized Cauchy and a general form of Hahn polynomials. We derive some q-identities such as: generating functions, extended generating functions, Mehler's formula and Roger's formula for these q-polynomials.

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The q-exponential operator

Cited by 7 publications

References 21 publications

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

Some homogeneous q-difference operators and the associated generalized Hahn polynomials

Some homogeneous $q$-difference operators and the associated generalized Hahn polynomials

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