R. Fuchs' problem of the Painleve equations from the first to the fifth

Details R. Fuchs' problem of the Painleve equations from the first to the fifth R. Fuchs' problem of the Painleve equations from the first to the fifth

2005-12-12

arxiv.org/abs/math/0512243v1

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

We will classify all rational transformations which change the confluent
hypergeometric equations to linear equations of the Painleve type from the
first to the fifth. We show such rational transformations correspond to almost
all of algebraic solutions of the Painleve equations from the first to fifth up
to the Backlund transformations.

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