On the transcendance of quasi-periodic Rosen continued fractions

Abstract In this paper, we consider the two Hecke groups $$G_{4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> and $$G_{6}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>6</mml:mn> </mml:msub> </mml:math> and we use the Schmidt Subspace Theorem to establish the transcendence of some quasi-periodic Rosen continued fractions in order to get the exact analogues of the results established with the regular continued fractions.