Chronological feed of everything captured from Stephen Clare.
Different Operators for the Polynomials $S_n(\delta, \zeta, \lambda|q)$ — , — Citations: 0.
The Homogeneous q-Shift Operator for Polynomials with Double q-Binomial Coefficients — Citations: 0.
Generalized q-difference equation for generalized Cigler's polynomials — This work establishes the generalized Cigler's polynomials and the generalized homogeneous q-shift operator. The q-difference equation is then utilized to demonstrate numerous polynomial q-identities, including the generating function and its extension, Rogers' formula and its extension, and Mehler's formula and its extension for the generalized Cigler's polynomials. Also presented a transformational identity involving generating functions for generalized Cigler's polynomials. — Citations: 0.
The Homogeneous q-Shift Operator for Cigler’s Polynomials — Citations: 0.
Generalized homogeneous q-shift operator applied for generalized Cigler's polynomials — In this paper, we establish the generalized homogeneous $q$-shift operator $E(q^\alpha z\theta_{xy})$ and the generalised Cigler's polynomials $\mathbb{D}^{(\alpha-n)}_n(\sigma_1, \cdots, \sigma_{r},\rho_1,\cdots, \rho_s,x,y,z)$. Then, we apply this operator to derive some $q$-identities such as: the generating function and its extension, Rogers formula and its extension, Mehler's formula and its extension, Srivastava-Agarwal type bilinear generating functions to the polynomials $\mathbb{D}^{(\a — Citations: 0.