On symmetric solutions of the fourth q-Painlev\'e equation
Abstract
The Painlev\'e equations possess transcendental solutions y(t) with special initial values that are symmetric under rotation or reflection in the complex t-plane. They correspond to monodromy problems that are explicitly solvable in terms of classical special functions. In this paper, we show the existence of such solutions for a q-difference Painlev\'e equation. We focus on symmetric solutions of a q-difference equation known as qPIV or q P(A5(1)) and provide their symmetry properties and solve the corresponding monodromy problem.
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