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

Jin Wang

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

Combinatorics 2019-05-28 v1

Authors: Jin Wang

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 ${}_1\psi_1$ summation formula as special cases.

Keywords

q-series and q-analogues special functions and series expansions ramanujan identities and series

Cite

@article{arxiv.1905.10513,
  title  = {A general q-expansion formula based on matrix inversions and its applications},
  author = {Jin Wang},
  journal= {arXiv preprint arXiv:1905.10513},
  year   = {2019}
}

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18pages

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

Abstract

Keywords

Cite

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