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arXiv · 1905.10513

A general q-expansion formula based on matrix inversions and its applications

Jin Wang
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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 $$\left\{z^n\frac{(az:q)_n}{(bz:q)_n}\bigg|n=0,1,2\cdots\right\}.$$ 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 ${}_1ψ_1$ summation formula as special cases.

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Jin Wang. 2019-05-25. A general q-expansion formula based on matrix inversions and its applications. https://arxiv.org/abs/1905.10513

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