Note on the Stern-Brocot sequence, some relatives, and their generating power series

Degree-One Mahler Functions: Asymptotics, Applications and Speculations

“…In terms of the polynomial coefficients in (1.1), r(z) = −a 1 (z)/a 0 (z). Due to this product representation, degree-one Mahler functions have been widely studied (see [5][6][7][8]14] for some recent work). Some of the strongest results in this area concern this class of functions: degree-one Mahler functions are either rational or hypertranscendental, that is, they do not satisfy algebraic differential equations with polynomial coefficients [4].…”