Some q-identities derived by the ordinary derivative operator.

In this paper, we investigate applications of the ordinary derivative operator, instead of the q-derivative operator, to the theory of q-series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the q-binomial theorem, Ramanujan's {}_1\psi _1 formula, the quintuple product identity, Gasper's q-Clausen product formula, and Rogers' {}_6\phi _5 formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein's theorem on Lambert series. [ABSTRACT FROM AUTHOR]