Algebraic Independence By A Method of Mahler

We establish a general algebraic independence theorem for the solutions of a certain kind of functional equations. As a particular application, we prove that for any real irrational£, the numbers ∞Σ 1 [hξ] αh1, …∞Σ 1 [hξ] αhh 1 1 are algebraically independent, for multiplicatively independent algebraic numbers α¡ with 0<|αi|<l. Subject classification (Amer. Math. Soc. (MOS) 1970): 10 F 35, 10 F 45, 39 A 30.