q-Differential operator identities and applications |
| |
| Authors: | Jian-Ping Fang |
| |
| Institution: | a Department of Mathematics, East China Normal University, Shanghai 200062, PR China
b Department of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu 223300, PR China |
| |
| Abstract: | In this paper, we construct a new q-exponential operator and obtain some operator identities. Using these operator identities, we give a formal extension of Jackson's  transformation formula. A formal extension of Bailey's  summation and an extension of the Sears terminating balanced  transformation formula are also derived by our operator method. In addition, we also derive several interesting a formal extensions involving multiple sum about three terms of Sears  transformation formula and Heine's  transformation formula. |
| |
| Keywords: | q-Series Basic hypergeometric series q-Differential operator q-Ultraspherical polynomials Big q-Laguerre polynomials |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
