A general q-expansion formula based on matrix inversions and its applications
Abstract
In this paper, by use of matrix inversions, we establish a general q-expansion formula of arbitrary formal power series F(z) with respect to the base \zn(az:q)n(bz:q)n|n=0,1,2·s\. Some concrete expansion formulas and their applications to q-series identities are presented, including Carlitz's q-expansion formula, a new partial theta function identity and a coefficient identity of Ramanujan's 11 summation formula as special cases.
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