A transformation and certain special values of hypergeometric series over finite fields

In this paper, we obtain a finite field analog for a transformation satisfied by 2F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_1$$\end{document}-classical hypergeometric series. We use properties of character sums over finite fields to deduce these results. Using these, we further evaluate certain special values for hypergeometric series over finite fields.