Another homogeneous q-difference operator |
| |
Authors: | Husam L Saad Abbas A Sukhi |
| |
Institution: | Department of Mathematics, College of Science, Basrah University, Basrah, Iraq |
| |
Abstract: | In this paper we show the equivalence between Goldman-Rota q-binomial identity and its inverse. We may specialize the value of the parameters in the generating functions of Rogers-Szegö polynomials to obtain some classical results such as Euler identities and the relation between classical and homogeneous Rogers-Szegö polynomials. We give a new formula for the homogeneous Rogers-Szegö polynomials hn(x,y|q). We introduce a q-difference operator θxy on functions in two variables which turn out to be suitable for dealing with the homogeneous form of the q-binomial identity. By using this operator, we got the identity obtained by Chen et al. W.Y.C. Chen, A.M. Fu, B. Zhang, The homogeneous q-difference operator, Advances in Applied Mathematics 31 (2003) 659-668, Eq. (2.10)] which they used it to derive many important identities. We also obtain the q-Leibniz formula for this operator. Finally, we introduce a new polynomials sn(x,y;b|q) and derive their generating function by using the new homogeneous q-shift operator L(bθxy). |
| |
Keywords: | Rogers-Szegö polynomials Cauchy polynomials Goldman-Rota q-binomial identity The homogeneous q-shift operator |
本文献已被 ScienceDirect 等数据库收录! |
|