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arXiv · 1707.08702

Differential transcendence of solutions of difference Riccati equations and Tietze's treatment

Seiji Nishioka
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Abstract

There is the paper by H. Tietze published in 1905 on differential transcendence of solutions of difference Riccati equations. In this paper, we clarify the essence of Tietze's treatment and make it purely algebraic. As an application, the $q$-Airy equation is studied.

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Seiji Nishioka. 2017-07-27. Differential transcendence of solutions of difference Riccati equations and Tietze's treatment. https://doi.org/10.1016/j.jalgebra.2018.06.008

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