Monodromy problem and boundary condition for some Painlevé equations

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  • Jimbo Michio
    Research Institute for Mathematical Sciences, Kyoto University

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  • Monodromy Problem and the Boundary Condition for Some Painlevé Equations

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Introduction The Painleve transcendents and their generalizations have aroused much interest among mathematicians and mathematical physicists in recent years ([l]-[8]). Yet their properties as special functions still remain almost unexplored. For example, the problem of determining their behavior at the fixed critical singularities is left open, except for a few special cases ([3] [4]). In the present paper we treat this problem for the following three kinds of Painleve equations at the fixed critical point i = 0 :

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