On quadratic differences that depend on the product of arguments -- revisited (Q1881594)

The paper is closely related to [loc. cit.]: \textit{J. K. Chung, B. R. Ebanks, C. T. Ng, P. K. Sahoo, W. B. Zheng}, [Results Math. 31, 53-74 (1997; Zbl 0879.39008)]. Here the domain of definition of the functions occurring in the equation is \(K \setminus \{0\}\) with \(K = \mathbb{R}\) or \(K = \mathbb{C}\), whereas in [loc. cit.] it is \(K\) itself. In this restricted domain new solutions containing a logarithmic term appear. Moreover, solving the equations requires an approach different from that presented in [loc. cit.].