Rational approximation to a new generalization of the Rogers-Ramanujan continued fraction (Q5928002)

The authors give an irrationality measure for the values at some rational points of the continued fraction NEWLINE\[NEWLINEG(x,y,z)=1+{xyz\over 1+} {xy^2 z^{2^2} \over 1+}{xy^3z^{3^2} \over 1+\cdots} {xy^nz^{n^2}\over 1+\cdots}NEWLINE\]NEWLINE and prove this irrationality measure to be best possible. The method is basically the same as in [\textit{I. Shiokawa}, Acta Arith. 50, 23-30 (1988; Zbl 0655.10031)]. See also \textit{D. Duverney} and \textit{I. Shiokawa} [Osaka J. Math. 37, 759-771 (2000; Zbl 0970.11027)].