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Preprints of the Keldysh Institute of Applied Mathematics, 2011, 066, 8 pp.
(Mi ipmp172)
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The Picard solution of the sixth Painlevé equation and asymptotic forms found by Power Geometry.
I. V. Goryuchkina
Abstract:
The sixth Painlevé equation has solutions, which in the generic case determined new transcendent functions [1] (Painlevé transcendents). Only for some values of complex parameters of the equation it is possible to write its solution, which is expressed in elementary or known special functions. One of the most famous solution of the sixth Painlevé equation is the Picard solution. By the methods of Power Geometry we found all asymptotic expansions of solutions to the sixth Painlevé equation for all values its complex parameters of the five types. The purpose of this work is: to compare the known solution with asymptotic forms, found by Power Geometry.
Citation:
I. V. Goryuchkina, “The Picard solution of the sixth Painlevé equation and asymptotic forms found by Power Geometry.”, Keldysh Institute preprints, 2011, 066, 8 pp.
Linking options:
https://www.mathnet.ru/eng/ipmp172 https://www.mathnet.ru/eng/ipmp/y2011/p66
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Abstract page: | 111 | Full-text PDF : | 63 | References: | 28 |
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