A note on the transcendency of Painlevé’s first transcendent-Reference-Cited by-同舟云学术

A note on the transcendency of Painlevé’s first transcendent

Published:1988-03 Issue: Volume:109 Page:63-67
ISSN:0027-7630
Container-title:Nagoya Mathematical Journal
language:en
Short-container-title:Nagoya Mathematical Journal

Author:

Nishioka Keiji

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference7 articles.

1. Sur les équations différentielles du second order à points critiques fixes;Liouville;Oevres de P. Painlevé,1975

2. On Galois Theory of Fields with Operators

3. A class of transcendental functions containing elementary and elliptic ones;Nishioka;Osaka J. Math,1985

4. Introduction to the Painlevé Equations (in Japanese);Okamoto;Sophia Kokyuroku in Math,1985

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