On finding formal power-logarithmic expansions of solutions to q-difference equations

2025/12/22 by Gaianov, Nikita, Parusnikova, Anastasia
#34m25 #34m55 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.19006

Abstract

An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation for specific values of the equation parameters is given; two different values of the number q are considered, leading to qualitatively different formal asymptotic expansions of the solutions of the fifth Painlevé equation.

Citations

• On the crystal limit of the q-difference sixth Painlevé equation

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