A Certain Power Series and the Inhomogeneous Continued Fraction Expansions Original Research Article

A recent paper (J. Number Theory42(1992), 61–87) announced various arithmetical properties of the Mahler functionf(θ, φ;x, y)=∑∞k=1∑1≤m≤kθ+φxkym. Unfortunately the arguments of that paper are marred by an error whereby the arguments hold only forφ=0 (or whenbn=1 for all positive integersn). We show how to correct the arguments so that they do hold for generalφ. Moreover, another paper (J. Number Theory43(1993), 293–318) soon afterwards happened again to discuss the subject using different expressions for the power series forf. We show that the corrected results here do coincide with those later results notwithstanding our alternative presentation