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A note on the transcendency of Painlevé’s first transcendent

Published online by Cambridge University Press:  22 January 2016

Keiji Nishioka
Keiji Nishioka*
Affiliation:
Takabatake-cho 184-632, Nara, 630, Japan
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Here we shall prove that Painlevé’s first transcendent, a solution of the equation y″ = 6y2 + x, can not be described as any combination of solutions of first order algebraic differential equations and those of linear differential equations. This result gives an answer to the question whether the function is truely new or not.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 109 , March 1988 , pp. 63 - 67
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

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