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Solutions of the third Painlevé equation I

Published online by Cambridge University Press:  22 January 2016

Hiroshi Umemura  and
Humihiko Watanabe
Hiroshi Umemura
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan, [email protected]
Humihiko Watanabe
Affiliation:
Graduate School of Mathematics, Kyushu University (at Ropponmatsu Branch), Chuo-ku, Fukuoka 810-8560, Japan
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Abstract.

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We classify transcendental classical solutions of the third Painlevé equation. This result combined with the list of algebraic solutions in [11] gives a complete table of classical solutions of the third Painlevé equation.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 1 - 24
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

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