Mean iterations derived from transformation formulas for the hypergeometric function (Q842320)

From Goursat's transformation formulae, the authors have deduced double sequences by iteration and expressed their common limits by invoking Gauss hypergeometric function \({}_2F_1(.)\). Theorem 2 and 3 (of this paper) are used to list pairs of means and their common limits, which are induced from quadratic and cubic transformations [see \textit{E. D. Rainville}, Special functions. Bronx, N. Y.: Chelsea Publishing Comp. (1971; Zbl 0231.33001), pp. 56--65]. Further, double sequences are obtained whose common limits can be expressed by \({}_3F_2(.)\). The reference [E], for [\textit{A. Erdélyi, W. Magnus, F. Oberhettinger} and \textit{F. G. Tricomi}, Higher transcendental functions. Vol. I, New York: McGraw-Hill Book Co. (1953; Zbl 0051.30303)], mentioned on p. 585, raises surprise and at the same time confusion, and are apparently incorrect. We know that from [\textit{A. Erdélyi, W. Magnus, F. Oberhettinger} and \textit{F. G. Tricomi}, Higher transcendental functions. Vol. II, New York-Toronto-London: McGraw-Hill Book Co. (1953; Zbl 0052.29502)] (whereas the authors cite 1981 as the year of its publication).