Certain inequalities for Appell's \(F_ 3\) and \(F_ 4\) (Q1184888)

Inequalities for Appell's functions \(F_ 1\), \(F_ 2\) and \(F_ 3\) were given by \textit{Y. L. Luke} [J. Approximation Theory 11, 73-84 (1974; Zbl 0276.33009)] for negative real arguments. Earlier, the authors [Jñānābha, Sect. A 9-10, 179-186 (1980; Zbl 0498.33006)] obtained inequalities for \(F_ 1\) and \(F_ 2\) for positive real arguments. In this paper, they obtain three inequalities for \(F_ 4\) for positive real arguments and also an inequality for \(F_ 3\).