Abstract
The first $q$-Painlevé equation has a unique formal solution around the infinity. This series converges only for $|q|=1$. If $q$ is a root of unity, this series expresses an algebraic function. In cases that all coefficients are integers, it can be represented by generalized hypergeometric series.
Citation
Yousuke Ohyama. "Expansions on special solutions of the first $q$-Painlevé equation around the infinity." Proc. Japan Acad. Ser. A Math. Sci. 86 (5) 91 - 92, May 2010. https://doi.org/10.3792/pjaa.86.91
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