Source: J. Math. Soc. Japan
Volume 64, Number 3
The discrete second Painlevé equation dPII is mapped to the second Painlevé equation PII by its continuous limit, and then, as shown by Kajiwara et al., a rational solution of dPII also reduces to that of PII. In this paper, regarding dPII as a difference equation, we present a certain asymptotic solution that reduces to a triply-truncated solution of PII in this continuous limit. In a special case our solution corresponds to a rational one of dPII. Furthermore we show the existence of families of solutions having sequential limits to truncated solutions of PII.
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