Expansions on special solutions of the first $q$-Painlevé equation around the infinity
Ohyama, Yousuke
Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, p. 91-92 / Harvested from Project Euclid
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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.
Publié le : 2010-05-15
Classification:  $q$-Painlevé equation,  hypergeometric series,  34M55,  33E17 
@article{1272289545,
     author = {Ohyama, Yousuke},
     title = {Expansions on special solutions of the first $q$-Painlev\'e equation around the infinity},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {86},
     number = {1},
     year = {2010},
     pages = { 91-92},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1272289545}
}

Ohyama, Yousuke. Expansions on special solutions of the first $q$-Painlevé equation around the infinity. Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, pp.  91-92. http://gdmltest.u-ga.fr/item/1272289545/