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

Seiji Nishioka

doi:10.1016/j.jalgebra.2018.06.008

paper

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

arXiv:1707.08702 · doi:10.1016/j.jalgebra.2018.06.008

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.

References in corpus (1)

Galois groups for integrable and projectively integrable linear difference equations