Algebraic Structure of Quasiradial Solutions to the Γ-harmonic Equation

We obtain an explicit representation for quasiradial γ-harmonic functions, which shows that these functions have essentially algebraic nature. In particular, we give a complete description of all γ which admit algebraic quasiradial solutions. Unlike the cases γ = ∞ and γ = 1, only finitely many algebraic solutions is shown to exist for any fixed |γ| > 1. Moreover, there is a special extremal series of γ which exactly corresponds to the well-known ideal m-atomic gas adiabatic constant γ = 2m+3 2m+1 .