Abstract:We consider a connection problem of the first Painlevé equation (P I ), trying to connect the local behavior (Laurent series) near poles and the asymptotic behavior as the variable t tends to negative infinity for real P I functions. We get a classification of the real P I functions in terms of (p, H) so that they behave differently at the negative infinity, where p is the location of a pole and H is the free parameter in the Laurent series. Some limiting-form connection formulas of P I functions are obtained … Show more
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