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 Φ 2 2 transformation formula. A formal extension of Bailey's ψ 3 3 summation and an extension of the Sears terminating balanced Φ 3 4 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 Φ 2 3 transformation formula and Heine's Φ 1 2 transformation formula.
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