On the non-quadraticity of values of the q-exponential function and related q-series. Acta Arith. 136 (2009), no. 3, 243–269.1730-6264 The authors are interested in the irrationality and the non-quadraticity (i.e., belonging to a quadratic extension of the rationals Q) properties of the function ∞ ∑ z F (z) = Fq(z; λ):= n ∏n j=1 (qj − λ), an entire function for any q ∈ C. For λ = 1, 0 this reduces to the q-exponential function ∞ ∑ z Eq(z) = n ∏n j=1 (qj − 1) and the so-called Tschakaloff function Tq(z) = n=0 n=0 n=0 q −n(n+1)/2 z n respectively, considered in earlier works ([P. Bundschuh, Invent. Math. 9 (1969/1970), 175
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