Turán type inequalities for \(q\)-hypergeometric functions (Q1949156)

The authors present a Turán-type inequality for the \(q\)-hypergeometric function \[ {}_2\phi_1 (q^a, q^{c-a},q^c; q, x) = \sum_{n=0}^\infty \frac{(q^a; q)_n (q^{c-a}; q)_n}{(q^c; q)_n (q; q)_n}\,x^n \] and the \(q\)-Kummer hypergeometric function \[ {}_1 \phi_1 (q^a, q^c; q, (1-q) x) = \sum_{n=0}^\infty \frac{(q^a; q)_n (1 - q)^n}{(q^c; q)_n (q; q)_n}\,x^n. \]