2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221219We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.5 pages, AMSTeXNumber TheoryClassical Analysis and ODEs11J72, 11J82 (Primary), 33D15 (Secondary)text