A finite field analogue of the Appell series \(F_4\) (Q2316276)

A finite field analogue of the Appell series \(F_1\) has been introduced by \textit{L. Li} et al. [Int. J. Number Theory 14, No. 3, 727--738 (2018; Zbl 1390.33026)]; that of \(F_2\) by \textit{B. He} et al. [Finite Fields Appl. 48, 289--305 (2017; Zbl 1373.33023)] and finally of \(F_3\) by \textit{B. He} (2017). All these analogues used integral representations of the corresponding Appel series. In the paper under review the authors establish the function \(F^*_4\) as a finite field analogue of the Appell series \(F_4\) by proving results over finite fields analogous to classical results satisfied by \(F_4\).