科研之友
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摘要
We show that the alternative discrete Painleve I equation (alt-dP(I)) has a unique solution which remains positive for all n >= 0. Furthermore, we identify this positive solution in terms of a special solution of the second Painleve equation (P-II) involving the Airy function Ai (t). The special-function solutions of P-II involving only the Airy function Ai (t) therefore have the property that they remain positive for all n >= 0 and all t >= 0, which is a new characterization of these special solutions of P-II and alt-dP(I).
- 出版日期2016
