q-Differential operator identities and applications

• DOI: 10.1016/j.jmaa.2006.10.087
• Publication Date: 2006-12-14T12:10:44Z
• Authors: Jian-Ping Fang
• Keywords: q-Ultraspherical polynomials; Applied Mathematics; Big q-Laguerre polynomials; q-Series; q-Differential operator; 0101 mathematics; Basic hypergeometric series; 01 natural sciences; Analysis

AbstractIn 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 Φ22 transformation formula. A formal extension of Bailey's ψ33 summation and an extension of the Sears terminating balanced Φ34 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 Φ23 transformation formula and Heine's Φ12 transformation formula.